{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian Mixture Model\n",
    "\n",
    "This is tutorial demonstrates how to marginalize out discrete latent variables in Pyro through the motivating example of a mixture model. We'll focus on the mechanics of parallel enumeration, keeping the model simple by training a trivial 1-D Gaussian model on a tiny 5-point dataset. See also the [enumeration tutorial](http://pyro.ai/examples/enumeration.html) for a broader introduction to parallel enumeration.\n",
    "\n",
    "#### Table of contents\n",
    "\n",
    "- [Overview](#Overview)\n",
    "- [Training a MAP estimator](#Training-a-MAP-estimator)\n",
    "- [Serving the model: predicting membership](#Serving-the-model:-predicting-membership)\n",
    "  - [Predicting membership using discrete inference](#Predicting-membership-using-discrete-inference)\n",
    "  - [Predicting membership by enumerating in the guide](#Predicting-membership-by-enumerating-in-the-guide)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from __future__ import print_function\n",
    "import os\n",
    "from collections import defaultdict\n",
    "import numpy as np\n",
    "import scipy.stats\n",
    "import torch\n",
    "from torch.distributions import constraints\n",
    "from matplotlib import pyplot\n",
    "%matplotlib inline\n",
    "\n",
    "import pyro\n",
    "import pyro.distributions as dist\n",
    "from pyro import poutine\n",
    "from pyro.contrib.autoguide import AutoDelta\n",
    "from pyro.optim import Adam\n",
    "from pyro.infer import SVI, TraceEnum_ELBO, config_enumerate, infer_discrete\n",
    "\n",
    "smoke_test = ('CI' in os.environ)\n",
    "assert pyro.__version__.startswith('0.3.0')\n",
    "pyro.enable_validation(True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "Pyro's [TraceEnum_ELBO](http://docs.pyro.ai/en/dev/inference_algos.html#pyro.infer.traceenum_elbo.TraceEnum_ELBO) can automatically marginalize out variables in both the guide and the model. When enumerating guide variables, Pyro can either enumerate sequentially (which is useful if the variables determine downstream control flow), or enumerate in parallel by allocating a new tensor dimension and using nonstandard evaluation to create a tensor of possible values at the variable's sample site. These nonstandard values are then replayed in the model. When enumerating variables in the model, the variables must be enumerated in parallel and must not appear in the guide. Mathematically, guide-side enumeration simply reduces variance in a stochastic ELBO by enumerating all values, whereas model-side enumeration avoids an application of Jensen's inequality by exactly marginalizing out a variable.\n",
    "\n",
    "Here is our tiny dataset. It has five points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = torch.tensor([0., 1., 10., 11., 12.])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training a MAP estimator\n",
    "\n",
    "Let's start by learning model parameters `weights`, `locs`, and `scale` given priors and data. We will learn point estimates of these using an [AutoDelta](http://docs.pyro.ai/en/dev/contrib.autoguide.html#autodelta) guide (named after its delta distributions). Our model will learn global mixture weights, the location of each mixture component, and a shared scale that is common to both components. During inference, [TraceEnum_ELBO](http://docs.pyro.ai/en/dev/inference_algos.html#pyro.infer.traceenum_elbo.TraceEnum_ELBO) will marginalize out the assignments of datapoints to clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 2  # Fixed number of components.\n",
    "\n",
    "@config_enumerate\n",
    "def model(data):\n",
    "    # Global variables.\n",
    "    weights = pyro.sample('weights', dist.Dirichlet(0.5 * torch.ones(K)))\n",
    "    scale = pyro.sample('scale', dist.LogNormal(0., 2.))\n",
    "    with pyro.plate('components', K):\n",
    "        locs = pyro.sample('locs', dist.Normal(0., 10.))\n",
    "\n",
    "    with pyro.plate('data', len(data)):\n",
    "        # Local variables.\n",
    "        assignment = pyro.sample('assignment', dist.Categorical(weights))\n",
    "        pyro.sample('obs', dist.Normal(locs[assignment], scale), obs=data)\n",
    "\n",
    "global_guide = AutoDelta(poutine.block(model, expose=['weights', 'locs', 'scale']))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To run inference with this `(model,guide)` pair, we use Pyro's [config_enumerate()](http://docs.pyro.ai/en/dev/poutine.html#pyro.infer.enum.config_enumerate) handler to enumerate over all assignments in each iteration. Since we've wrapped the batched Categorical assignments in a [pyro.plate](http://docs.pyro.ai/en/dev/primitives.html#pyro.plate) indepencence context, this enumeration can happen in parallel: we enumerate only 2 possibilites, rather than `2**len(data) = 32`. Finally, to use the parallel version of enumeration, we inform Pyro that we're only using a single [plate](http://docs.pyro.ai/en/dev/primitives.html#pyro.plate) via `max_plate_nesting=1`; this lets Pyro know that we're using the rightmost dimension [plate](http://docs.pyro.ai/en/dev/primitives.html#pyro.plate) and that Pyro can use any other dimension for parallelization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "optim = pyro.optim.Adam({'lr': 0.1, 'betas': [0.8, 0.99]})\n",
    "elbo = TraceEnum_ELBO(max_plate_nesting=1)\n",
    "svi = SVI(model, global_guide, optim, loss=elbo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before inference we'll initialize to plausible values. Mixture models are very succeptible to local modes. A common approach is choose the best among many randomly initializations, where the cluster means are initialized from random subsamples of the data. Since we're using an [AutoDelta](http://docs.pyro.ai/en/dev/contrib.autoguide.html#autodelta) guide, we can initialize one param for each variable, where the name is prefixed by \"auto_\" and the constraint is appropriate for each distribution (you can find constraint from the [Distribution.support](https://pytorch.org/docs/stable/distributions.html#torch.distributions.distribution.Distribution.support) attribute)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed = 7, initial_loss = 25.6655845642\n"
     ]
    }
   ],
   "source": [
    "def initialize(seed):\n",
    "    pyro.set_rng_seed(seed)\n",
    "    pyro.clear_param_store()\n",
    "    # Initialize weights to uniform.\n",
    "    pyro.param('auto_weights', 0.5 * torch.ones(K), constraint=constraints.simplex)\n",
    "    # Assume half of the data variance is due to intra-component noise.\n",
    "    pyro.param('auto_scale', (data.var() / 2).sqrt(), constraint=constraints.positive)\n",
    "    # Initialize means from a subsample of data.\n",
    "    pyro.param('auto_locs', data[torch.multinomial(torch.ones(len(data)) / len(data), K)]);\n",
    "    loss = svi.loss(model, global_guide, data)\n",
    "    return loss\n",
    "\n",
    "# Choose the best among 100 random initializations.\n",
    "loss, seed = min((initialize(seed), seed) for seed in range(100))\n",
    "initialize(seed)\n",
    "print('seed = {}, initial_loss = {}'.format(seed, loss))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "During training, we'll collect both losses and gradient norms to monitor convergence. We can do this using PyTorch's `.register_hook()` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "...................................................................................................\n",
      "..................................................................................................."
     ]
    }
   ],
   "source": [
    "# Register hooks to monitor gradient norms.\n",
    "gradient_norms = defaultdict(list)\n",
    "for name, value in pyro.get_param_store().named_parameters():\n",
    "    value.register_hook(lambda g, name=name: gradient_norms[name].append(g.norm().item()))\n",
    "\n",
    "losses = []\n",
    "for i in range(200 if not smoke_test else 2):\n",
    "    loss = svi.step(data)\n",
    "    losses.append(loss)\n",
    "    print('.' if i % 100 else '\\n', end='')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(10,3), dpi=100).set_facecolor('white')\n",
    "pyplot.plot(losses)\n",
    "pyplot.xlabel('iters')\n",
    "pyplot.ylabel('loss')\n",
    "pyplot.yscale('log')\n",
    "pyplot.title('Convergence of SVI');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aSr9+/WjQoAGZmZkcOnSIdevWUatWLd18wUcNHjyYX375hR07djBo0KAXYiFrIUTlJz1dQghRTvr06cPZs2cZOHAgO3fuZPz48UycOJE///yTV155hRMnTvDmm28+sR1DQ0P++usvGjduzMyZM/niiy9wc3Pjl19+yXds9+7d+f3339FoNEyZMoWNGzeyfPly3XCuotjZ2XH06FGGDx/Oxo0bGTt2LAsWLODevXvMmjXrqd6D0aNHM3DgQJYvX87AgQP58MMPn6qdx3l6enLgwAG8vLx074mLi4suaXwe3n//fZKTk/n2228ZM2YMmzZtYty4cYUWScllYmJCQEAAXbt2ZeHChcyYMYM2bdoUmCx269aNefPmcfnyZSZMmMDhw4fZsmVLsZL10mBmZsaePXvo2LEjCxYsYMaMGbRt25bPPvsMoNAhlLnmzp1Lhw4d2LZtG/7+/vj7+3P06FFGjx5NcHBwgYsmd+zYUbeguAwtFEJUFiqlrGbECiGEEOKFNH/+fCZOnMiNGzdwcnIq73CEEKLcSdIlhBBCiKeWlpaWpypieno6TZo0QaPRcPny5XKMTAghKg6Z0yWEEEKIp/bqq69Ss2ZNGjduTGJiIr/++isXL15k1apV5R2aEEJUGJJ0CSGEEOKpdevWjWXLlrFq1So0Gg0eHh6sXbuWAQMGlHdoQghRYcjwQiGEEEIIIYQoQ1K9UAghhBBCCCHKkCRdQgghhBBCCFGGXog5Xf369SMwMJBOnTqxfv36Ep2bk5PDzZs3MTc3f+Iij0IIIYQQQoh/LkVRuH//Po6OjujpFb//6oWY0xUYGMj9+/f5+eefS5x03bhxA2dn5zKKTAghhBBCCFHZXL9+vUQL0b8QPV2+vr4EBgY+1bnm5uaA9o21sLAoxaiEEEIIIYQQlUlSUhLOzs66HKG4KnzStX//fubMmUNISAgxMTH88ccf9O3bN88xixcvZs6cOdy6dYtGjRqxcOFCWrZsWSrXzx1SaGFhIUmXEEIIIYQQosTTjip8IY2UlBQaNWrE4sWLC9y/bt06/P39+fzzzzlx4gSNGjWiW7du3L59+6mul5GRQVJSUp6HEEIIIYQQQjytCp90+fn5MWPGDPr161fg/m+//ZaRI0cyfPhwPDw8+OGHHzAxMeGnn356quvNnDkTS0tL3UPmcwkhhBBCCCGeRYVPuoqSmZlJSEgInTt31m3T09Ojc+fOHD58+KnanDJlComJibrH9evXSytcIYQQQgghxAuows/pKkpcXBwajQY7O7s82+3s7Lh48aLudefOnTl9+jQpKSnUqFGD33//HR8fnwLbNDIywsjIiMWLF7N48WI0Gk2Z3oMQQgghhCg7iqKQnZ0t3+lEsejr62NgYFDqS0VV6qSruHbv3l3ic8aMGcOYMWNISkrC0tKyDKISQgghhBBlKTMzk5iYGFJTU8s7FFGJmJiY4ODggFqtLrU2K3XSVa1aNfT19YmNjc2zPTY2Fnt7+2dqW3q6hBBCCCEqr5ycHCIiItDX18fR0RG1Wl3qvRfin0VRFDIzM7lz5w4RERG4ubmVaAHkolTqpEutVtOsWTMCAgJ0ZeRzcnIICAhg7Nixz9S29HQJIYQQQlRemZmZ5OTk4OzsjImJSXmHIyqJKlWqYGhoSGRkJJmZmRgbG5dKuxU+6UpOTiY8PFz3OiIiglOnTmFtbU3NmjXx9/dn6NChNG/enJYtWzJ//nxSUlIYPnz4M11XerqEEEIIISq/0uqpEC+OsvjMqBRFUUq91VIUGBhIhw4d8m0fOnQoK1asAGDRokW6xZEbN27M//73P1q1alUq18/t6UpMTJTFkYUQQgghKon09HQiIiKoXbt2qfVWiBdDUZ+dp80NKnxPl6+vL0/KC8eOHfvMwwkfV9l7uu7cz+BGfCoxiencTEjjXkomWZocsjQKWZocDPX1MDbUx9hQD1O1AVVN1VibGlLVRI21qZqqpmrMjUq/cosQQgghhBAvmgqfdJWXyjSnS1EUQmOSOHzlLiejEjgRFU9MYvozt2uor8LaVI2TVRWcqprgZFWF2tVMcLMzx7W6GRbGhqUQvRBCCCGEEKBSqfjjjz90tRr+SSTpqqQ0OQono+LZcf4W28/f4vq9tDz79VRgb2GMg1UVHK2qYGOqxshADwN9FQZ6emTn5JCelUNaloaUjGziU7OIT8nk3oNHWpaGLI1CbFIGsUkZnIhKyBeDo6UxjZytaFqzKk1qWuHlZImxof7zeguEEEIIIUQhVqxYwYQJE0hIyP8dTjx/knQVoiIOL7x+L5UDYXEcCLtDUHgcSenZun1GBnq0rmtD81rWNKlpRaMaVpgaPf2vNy1TQ3xqJnfuZxCdkMaN+FRuxKdx9U4KYbfvE5uUwc3EdG4m3uLvc7cAqGKoTxu3anRsUJ2ODapjZyHjp4UQQgghhJByLoUYM2YMoaGhHDt2rLxDAeDKnWTazt7Lv/44y9/nbpGUno2FsQF9Gzvyw+CmnJzWheXDWzKmgyut61Z7poQLoIpaH0erKjRytqJHQwfea1eX//Tx4tcRrQj+V2dOf96Vde+9xKd+DejqYUc1MyPSsjTsCo1lysaztPo6gEHLjrD1TAyZ2Tml9C4IIYQQQjw9RVFIzcwul0dJa9dt376dNm3aYGVlhY2NDT179uTKlSuAttCcSqXK04t16tQpVCoV165dIzAwkOHDh5OYmIhKpUKlUjF9+nQA4uPjGTJkCFWrVsXExAQ/Pz/CwsKKFVNkZCS9evWiatWqmJqa4unpybZt23T7z58/T8+ePbGwsMDc3Jy2bdvqYj527BhdunShWrVqWFpa0r59e06cOFHk9a5fv84bb7yBlZUV1tbW9OnTh2vXrpXgXaw4pKerkqhTzRQnqyo4WhnT1s2Wtm7VaOhkiYF++eTNllUMaVXHhlZ1bICH88r2XLhNwMXbnL6RQFD4XYLC71LNTM1bLWsyom0dLKvIPDAhhBBClI+0LA0e03aUy7VD/9MNE3Xxv3qnpKTg7++Pt7c3ycnJTJs2jX79+nHq1Kknntu6dWvmz5/PtGnTuHTpEgBmZmYADBs2jLCwMDZv3oyFhQWTJ0+mR48ehIaGYmhY9Pe0MWPGkJmZyf79+zE1NSU0NFTXbnR0NO3atcPX15c9e/ZgYWFBUFAQ2dnakVn3799n6NChLFy4EEVRmDdvHj169CAsLAxzc/N818rKyqJbt274+Phw4MABDAwMmDFjBt27d+fMmTOo1epiv5cVgSRdhahowwtVKhWBH/tiWE5J1pOoVCo8HS3xdLTkw05uXL+Xyrpj11l3/Dp37mewcE84vxyO5APfugz1qUUVtcz9EkIIIYQoTP/+/fO8/umnn7C1tSU0NPSJ56rVaiwtLVGpVNjb2+u25yZbQUFBtG7dGoBVq1bh7OzMpk2beP3114tsNyoqiv79+9OwYUMA6tSpo9u3ePFiLC0tWbt2rS55q1evnm5/x44d87T1448/YmVlxb59++jZs2e+a61bt46cnByWLVumq6a9fPlyrKysCAwMpGvXrk98HyoSSboKURGrF1bUhKsgztYmTOpWn/Gd3dh5PpYFAZe5HJvMN39f5KeDEUzr5UFPb8fyDlMIIYQQL5AqhvqE/qdbuV27JMLCwpg2bRrBwcHExcWRk6OdrhEVFYWJiclTxXDhwgUMDAzyrGdrY2ND/fr1uXDhwhPPHzduHB988AE7d+6kc+fO9O/fH29vb0A7vLFt27aF9pbFxsYydepUAgMDuX37NhqNhtTUVKKiogo8/vTp04SHh+frBUtPT9cNWaxMJOkSZcpQX49XvB3o7mXPppPRfLvrMtEJaYxdfZLdobF80cdLhhwKIYQQ4rlQqVQlGuJXnnr16oWLiwtLly7F0dGRnJwcvLy8yMzM1A3pe3SeWFZWVpnHNGLECLp168bWrVvZuXMnM2fOZN68eXz44YdUqVKlyHOHDh3K3bt3WbBgAS4uLhgZGeHj40NmZmaBxycnJ9OsWTNWrVqVb5+trW2p3M/zVHm6TkSlpq+non+zGuyZ1J5xHV3RU8GmUzfxm7+fQ1fiyjs8IYQQQogK4+7du1y6dImpU6fSqVMn3N3diY+P1+3PTTpiYmJ02x6f66VWq/NNk3F3dyc7O5vg4OB81/Lw8ChWbM7OzowaNYqNGzfy0UcfsXTpUgC8vb05cOBAoclfUFAQ48aNo0ePHnh6emJkZERcXOHfAZs2bUpYWBjVq1fH1dU1z6OijEIrCUm6xHNlZKCPf9f6/D6qNS42JtxMTGfwsmB+P369vEMTQgghhKgQqlatio2NDT/++CPh4eHs2bMHf39/3X5XV1ecnZ2ZPn06YWFhbN26lXnz5uVpo1atWiQnJxMQEEBcXBypqam4ubnRp08fRo4cycGDBzl9+jSDBw/GycmJPn36PDGuCRMmsGPHDiIiIjhx4gR79+7F3d0dgLFjx5KUlMSbb77J8ePHCQsLY+XKlbpCHm5ubqxcuZILFy4QHBzMoEGDiuwdGzRoENWqVaNPnz4cOHCAiIgIAgMDGTduHDdu3Hiat7VcSdJViMWLF+Ph4UGLFi3KO5R/pGYuVdk2ri39mjiRo8DH68/wfwcjyjssIYQQQohyp6enx9q1awkJCcHLy4uJEycyZ84c3X5DQ0PWrFnDxYsX8fb2ZtasWcyYMSNPG61bt2bUqFEMGDAAW1tbZs+eDWiLUTRr1oyePXvi4+ODoihs27btiZULATQaDWPGjMHd3Z3u3btTr149vvvuO0A7N2zPnj0kJyfTvn17mjVrxtKlS3Xt/t///R/x8fE0bdqUt99+m3HjxlG9evVCr2ViYsL+/fupWbMmr776Ku7u7rz77rukp6djYWFR4ve0vKmUki4a8ILJLaSRmJhYKX/BFZ2iKHy97QJLD2gTrnEdXZnYpZ6uSo0QQgghxNNIT08nIiKC2rVrY2xsXN7hiEqkqM/O0+YG0tMlypVKpeJfPdz5uFt9AP63J5xvd10u56iEEEIIIYQoPZJ0iXKnUqkY08GV//TxBGDhnnD2XrpdzlEJIYQQQrxY/Pz8MDMzK/Dx9ddfl3d4lVrlqJkpXghDfGoRfjuZXw5H8tFvp9k2ri32ljIcQAghhBDieVi2bBlpaWkF7rO2tn7O0fyzSNIlKpR/9XAnJDKe8zeTGLf2JKtHtMKgEi0KLYQQQghRWTk5OZV3CP9Y8m22EFK9sHwYG+qzaGBTTNX6HI24x/8Cwso7JCGEEEIIIZ6JVC98AqleWD42n77JuDUnUalgy4dt8HQs3UXwktKz2HvxNnsu3iYxLQtrEzVVTdVUMzOiR0N7XGxMS/V6QgghhHi+pHqheFplUb1QhheKCql3I0d2nLvF1rMxLDsQwX8HNC6Vdk9dT2DezkscuXqXLE3Bf2+Ys+Mir3g7Mqp9nVJP9oQQQgghxItHki5RYY1qX5etZ2P46/RNPuleHwfLwlctL46/Tt/ko99Pk5mdA0BdW1O6eNhTp5op8amZ3EvNJPRmEgfC4vjr9E3+On2Tzu52zHnNm6qm6tK4JSGEEEII8QKSpEtUWA1rWPJSHWuOXL3HiqBrTOnh/lTtKIrCd4FXmLPjEgCd3avzrx7u1LE1K/D40JtJ/LDvClvO3GT3hVj6fhfEsiHNcbMzf+p7EUIIIYQQL64XopDGli1bqF+/Pm5ubixbtqy8wxElMLJtHQBWB0dxPz2rxOcrisKUjWd1Cdc7L9dmydvNC024ADwcLfjfW03YNr4tztZViLybSr/vDrH3oqwdJoQQQogX14oVK7CysirvMCqlf3zSlZ2djb+/P3v27OHkyZPMmTOHu3fvlndYopg61K9OHVtT7mdks+7Y9RKfv+3sLdYeu46eCr7s48m0Xh7o66mKdW4Dewv+HNOGlrWtSc7I5p2fj7HuWFSJYxBCCCGEeN4kQapY/vFJ19GjR/H09MTJyQkzMzP8/PzYuXNneYcliklPT8WINtreruVB18jW5BT73GxNDvN2aXu4xnZ0422fWiW+vrWpml/fbcVbLZ1RFPjXH+c4FB5X4naEEEIIIcSLq8InXfv376dXr144OjqiUqnYtGlTvmMWL15MrVq1MDbJTvQvAAAgAElEQVQ2plWrVhw9elS37+bNm3kWenNyciI6Ovq5xC5Kx6tNnbAxVROdkMa2c7eKfd6GEze4eieFqiaGjGxb+6mvrzbQ4+t+Denb2BFNjsIHq04QEZfy1O0JIYQQopwoCmSmlM+jhKs0bd++nTZt2mBlZYWNjQ09e/bkypUrAAQGBqJSqUhISNAdf+rUKVQqFdeuXSMwMJDhw4eTmJiISqVCpVIxffp0AOLj4xkyZAhVq1bFxMQEPz8/wsKefl3U77//nrp166JWq6lfvz4rV67Msz8hIYH3338fOzs7jI2N8fLyYsuWLQBERkbSq1cvqlatiqmpKZ6enmzbtu2pY6nIKnwhjZSUFBo1asQ777zDq6++mm//unXr8Pf354cffqBVq1bMnz+fbt26cenSJapXr14OEYvSZmyoz9s+LszfHcaa4Ch6N3J84jnpWRrm79b+B2RMB1fMjQ2fKQaVSsU3/b2JvJfKyagE3v35GH+MfhnLKs/WrhBCCCGeo6xU+PrJ3yPKxL9ugrr464CmpKTg7++Pt7c3ycnJTJs2jX79+nHq1Kknntu6dWvmz5/PtGnTuHRJO+rHzEw7n33YsGGEhYWxefNmLCwsmDx5Mj169CA0NBRDw5J9r/njjz8YP3488+fPp3PnzmzZsoXhw4dTo0YNOnToQE5ODn5+fty/f59ff/2VunXrEhoair6+PgBjxowhMzOT/fv3Y2pqSmhoqC7Of5oKn3T5+fnh5+dX6P5vv/2WkSNHMnz4cAB++OEHtm7dyk8//cSnn36Ko6Njnp6t6OhoWrZsWWh7GRkZZGRk6F4nJSWVwl2IZ9WjoQPzd4dx6noC2ZocDPSL7qT99UgkMYnpOFgaM/gll1KJwdhQnyVvN6PvoiCu3klh7OoTrBjesthzxIQQQgghiqt///55Xv/000/Y2toSGhr6xHPVajWWlpaoVCrs7e1123OTraCgIFq3bg3AqlWrcHZ2ZtOmTbz++uslinHu3LkMGzaM0aNHA+Dv78+RI0eYO3cuHTp0YPfu3Rw9epQLFy5Qr149AOrUqaM7Pyoqiv79+9OwYcN8+/5pKnzSVZTMzExCQkKYMmWKbpuenh6dO3fm8OHDALRs2ZJz584RHR2NpaUlf//9N5999lmhbc6cOZMvvviizGMXJVPX1gxTtT4pmRrC7yTTwL7wFcDvp2exeG84ABM6u2FsqF9qcVQ3N2bZ0Ba89sMhDoTFsfZYFINalU5SJ4QQQogyZmii7XEqr2uXQFhYGNOmTSM4OJi4uDhycrTz2qOiojAxKVlbuS5cuICBgQGtWrXSbbOxsaF+/fpcuHDhqdp777338mx7+eWXWbBgAaAd8lijRg1dwvW4cePG8cEHH7Bz5046d+5M//798fb2LnEclUGFn9NVlLi4ODQaDXZ2dnm229nZceuWdu6PgYEB8+bNo0OHDjRu3JiPPvoIGxubQtucMmUKiYmJzJ07l/r16+Pq6lqm9yCKR19PhZeTJQBnricWeezyoGvEp2ZRx9aU/k1rlHosHo4WfNKtPgBzdlwiPiWz1K8hhBBCiDKgUmmH+JXHQ1WykTG9evXi3r17LF26lODgYIKDgwFtp4OenvYrvPLIPLGsrJIvrVPWqlSpUuT+ESNGcPXqVd5++23Onj1L8+bNWbhw4XOK7vmq1ElXcfXu3ZvLly8THh6eLxt/nJGRERYWFnz00UdcvHiRkJCQ5xSleJJGztqyp6duJBR53O4LsQB80L7uE4chPq3BL7nQwN6chNQs5u68VCbXEEIIIcSL6e7du1y6dImpU6fSqVMn3N3diY+P1+23tbUFICYmRrft8blearUajUaTZ5u7uzvZ2dm6BO7Ra3l4eJQ4Tnd3d4KCgvJsCwoK0rXl7e3NjRs3uHz5cqFtODs7M2rUKDZu3MhHH33E0qVLSxxHZVCpk65q1aqhr69PbGxsnu2xsbF5xq8+jcWLF+Ph4UGLFi2eqR1RehrV0CZdZ4pIutKzNFyI0c7De6lO4T2az8pAX48vensCsPpoFOeii+59E0IIIYQorqpVq2JjY8OPP/5IeHg4e/bswd/fX7ff1dUVZ2dnpk+fTlhYGFu3bmXevHl52qhVqxbJyckEBAQQFxdHamoqbm5u9OnTh5EjR3Lw4EFOnz7N4MGDcXJyok+fPiWO8+OPP2bFihV8//33hIWF8e2337Jx40YmTZoEQPv27WnXrh39+/dn165dRERE8Pfff7N9+3YAJkyYwI4dO4iIiODEiRPs3bsXd3f3Z3jnKq5KnXSp1WqaNWtGQECAbltOTg4BAQH4+Pg8U9tjxowhNDSUY8eOPWuYpSY5M5nQu0+ePPlP5V1DO7zwYsx90rM0BR5zISaJLI2CjamaGlWL7tJ+Vq3q2NC7kSOKAtP+PEdOTslKwQohhBBCFERPT4+1a9cSEhKCl5cXEydOZM6cObr9hoaGrFmzhosXL+Lt7c2sWbOYMWNGnjZat27NqFGjGDBgALa2tsyePRuA5cuX06xZM3r27ImPjw+KorBt27YSVy4E6Nu3LwsWLGDu3Ll4enqyZMkSli9fjq+vr+6YDRs20KJFC9566y08PDz45JNPdD1wGo2GMWPG4O7uTvfu3alXrx7ffffdU7xjFZ9KUUq4aMBzlpycTHi4tihCkyZN+Pbbb+nQoQPW1tbUrFmTdevWMXToUJYsWULLli2ZP38+v/32GxcvXsw316skFi9ezOLFi9FoNFy+fJnExEQsLAov3lDWLt27xKjdo9BT6fFX378wKeFkzH8CRVFoPmM3d1My2Ti6NU1rVs13zIqgCKb/FUrHBtX5aVjZ91LeSkyn47xAUjM1zH29Ea81K/05ZEIIIYQoufT0dCIiIqhduzbGxsblHY6oRIr67CQlJWFpaVni3KDC93QdP36cJk2a0KRJE0BbirJJkyZMmzYNgAEDBjB37lymTZtG48aNOXXqFNu3b3+mhAsqXk9XLctaGOsbczv1Nj+c+aG8wykXKpVK19t15nrBQwzP3NAO88s9rqzZWxrzYUc3AL4LDKeC/w1DCCGEEEKUgwqfdPn6+qIoSr7HihUrdMeMHTuWyMhIMjIyCA4OzlMG85/CSN+IT1t+CsDK0JVcTbxazhGVD2/dvK6C51DlFtnILbrxPLzt44KJWp+rd1I4di3+yScIIYQQQlRAfn5+mJmZFfj4+uuvyzu8Sq1Sr9NVlh4dXlhRtHduT7sa7dh/Yz/fBH/Dki5LUJWw/Ghl17iICoaJaVlcvZMCPCy68TyYGRnQ09uB347fYO2xKFrWtn5u1xZCCCGEKC3Lli0jLS2twH3W1vL95llU+J6u8lLRhhfm+rTFpxjqGXI45jABUQFPPuEfJnfY4NU7KSSl512P4uyD3q+a1iZYm6qfa1xvtqwJwLazMSSmVbx1MoQQQgghnsTJyQlXV9cCH5J0PRtJugpRUUvGO1s4M9xrOACzj80mLbvgv0b8U9mYGemqEp57bIjh6XIYWpiribMV9e3MSc/K4c9T0c/9+kIIIYQQouKSpKsQFbWnC2BEwxE4mDoQkxLDqguryjuc5y536ODjQwxPPyiu0eg5FdF4lEql4s2WzgCsOXq91ApqJKRmEhQexw/7rvCvP87yXWA4u0NjibqbKiXqhRBCCCEqCZnTVQlVMajCe97v8cXhL9gTtYcRDUeUd0jPVSNnS9LOb8XzxFrw+R6MzIDy7ekC6NfEiZl/X+RCTBJnoxN1RT+exrnoRKZsPMvZIhZddrKqwge+dXmjuTNqA/n7iRBCCCFERSXf1Cqptk5tATgXd46E9ILLp/9TtTK7zXeGC2iftBmCvwe062XFJmWgr6fC07F81lOzMlHj52UPwNpj15+qDU2OwuK94fRdHKRLuGpam9CjoT2jfevSu5EjDezNUevrEZ2QxtRN5+gwN5BVwZFkaXJK7V6EEEIIIUTpkZ6uQlTE6oWPsjO1w9XKlfCEcI7cOkL3Wt3LO6TiS0uA26Fw+wLcuQhVrKH9J6Cn/+RzszPwOvIR+iptsQpN8I/otx7HqQdDC+vZmWOifuxjfXY9mNlB7balfSf5vNmiJn+eusnmUzf5dw93TI2K/0/sZkIa49ac5Hiktux8d097/tPXk+rm+Rd0TM/SsPZoFN8FXiE6IY1//3GOzadu8sPgZlR9zkVEhBBCCCFE0aSnqxAVeU5XrtaOrQE4fPNwOUdSAqdWw1w3WO4HW/3h6I+w7xvYP6d45+/+Av3b50lQWRKrWKGfchvNmQ26oYWNnR+bz3XnMmx4F1b2hWtBpXwz+b1Uxxpn6yokZ2Rz5OrdYp+nyVEY9WsIxyPjMTMyYO7rjfh+cNMCEy4AY0N9hr1cm/2fdGBaTw/MjAwIjrhH3++CCL+dXFq3I4QQQghRZqZPn07jxo1LdI6vry8TJkwoo4jKjiRdlVhu0hUUHVRqhRvKVORh2DwONJlgUQNcu4D3m9p9gd/A1X1Fnx8eAEcWa5/6fMPPGm3v3s3tcwmJuAeQfx7VjQdJc042/DYEEm+U2u0URKVS0aKWtqTqueikYp+38vA1ztxIxNzYgK3j2vBasxrFWoPN2FCfd9rUZsMHrXGyqkLk3VT6fRfEgbA7T3sLQgghhPgHWLFiBVZW5TPPvbgmTZpEQEDpL4GkUqnYtGlTqbf7LGR4YSXWzK4Zaj01samxRCRGUMeqzhPPSc1KZcX5FUQkRpCSGkdKSixWOQr+Vo1xMTQHVGBTF2q1BQuH0gs24TqsGww5WeDRF15fAblJhb4BnPwVNoyAUQfB3K6AwO/Bpg+0z1uMoHnXgSRWa0rqn3/gnHkF/esHAc/8iyLHnH6kjThYOwje2Q6GVUrv3h7j5WjJxhPRRRbBeNStxHTm7rwMwCfdG+BiY1ria9a3N+fPsS/z/soQQiLjeWfFMdaMfInmtWRNDSGEEEJUTGZmZpiZmZV3GM+F9HQVoqKu0/UoYwNjmtk1AyDoZvGGzn21ZwLfn/6e7de2c+D2cU6kXGdP2g3eurGZQ0cXaIf6bRwJ3zaAhc1g6ySIv/ZsgWamwNq3tEmPfUPo+93DhAvAbw7YukPKbe21cwqYR3dhMyTHgo0rdJ0BQKemDUio/wYAI/S3YWyoRz27x/7hxpzS/uwwVTt3LOYUbJkIZdgz2PBByfrzN4uXdH3x13mSM7Jp7GzFoAeLLD+NamZGrBrRii4edmRpFEb9eoJbielP3Z4QQgghys/27dtp06YNVlZW2NjY0LNnT65cuQJAYGAgKpWKhISHxdROnTqFSqXi2rVrBAYGMnz4cBITE1GpVKhUKqZPnw5AfHw8Q4YMoWrVqpiYmODn50dYWNgT41EUBVtbW9avX6/b1rhxYxwcHv6R/uDBgxgZGZGamgpAQkICI0aMwNbWFgsLCzp27Mjp0w//IP748MLs7GzGjRunu+fJkyczdOhQ+vbtmyeWnJwcPvnkE6ytrbG3t9fdG0CtWrUA6NevHyqVSvf69OnTdOjQAXNzcywsLGjWrBnHjx9/4n2XFkm6ClEZ5nQBvOz0MgCHbh4q/CBFgYgD/P1zBzbfOoyeovDhvQT+E5fAnGxLGhlYcF9fjw/sq/OLZ0cUh0ag0oO74XBsKSxqATunagtgPI3NH8Kts2BSDd5cA+rHenLUJvDGz2BoAhH74PCi/G1EPrg/z1fz9FI5dpuIgopO+icZ5ZmDgf4jH+kcjfa6AB694fXloNKH02sgtOy6nN0dLFCpICYxnbjkjCKP3R0ay9/nbqGvp2Lmqw3R03vykMKiGBvqM39AYxrYmxOXnMH7v4aQnlUxi8EIIYQQz5uiKKRmpZbLo6RTQVJSUvD39+f48eMEBASgp6dHv379yMl5crXi1q1bM3/+fCwsLIiJiSEmJoZJkyYBMGzYMI4fP87mzZs5fPgwiqLQo0cPsrKyimxTpVLRrl07AgMDAW3yduHCBdLS0rh48SIA+/bto0WLFpiYmADw+uuvc/v2bf7++29CQkJo2rQpnTp14t69ewVeY9asWaxatYrly5cTFBREUlJSgcMEf/75Z0xNTQkODmb27Nn85z//YdeuXQC67+7Lly8nJiZG93rQoEHUqFGDY8eOERISwqeffoqhoeET38vSIsMLKzkfRx8Ajt86ToYmAyN9o7wHpCfBxve4eXUnXzo6gL4e71WpxXsd/g2OTcDQmI6aTL488iWbwjcxJzWc202HMslrszbROboErgbCoYVwchV0/RKaDC5+gBH74dwG0DOAASvByrng42zra3uwtvprhxq+PP7hPkV5WASj1st5z7Opi6q+H1zaxgTTXcArD/fFXYasVDA01faQ2daHVqO088LCdoNnv7xtKQokXtfON9N7+r9HmBkZULuaKVfvpHD+ZhLt69kWeFx6lobPN58HYESb2rg7lE6pe1MjA358uzm9Fh3k9PUEpv15jln9vYs1R0wIIYT4J0vLTqPV6lblcu3ggcGYGJoU+/j+/fvnef3TTz9ha2tLaGjoE89Vq9VYWlqiUqmwt7fXbQ8LC2Pz5s0EBQXRurW2NsCqVatwdnZm06ZNvP7660W26+vry5IlSwDYv38/TZo0wd7ensDAQBo0aEBgYCDt27cHtL1eR48e5fbt2xgZab+fzp07l02bNrF+/Xree++9fO0vXLiQKVOm0K+f9jvaokWL2LZtW77jvL29+fzzzwFwc3Nj0aJFBAQE0KVLF2xttd+7rKys8tx7VFQUH3/8MQ0aNNCd9zxJT1cl52blhm0VW9I16Zy8fTLvzvhI+L+uaC7/zRRbW+7r6+FdtQHvv74JXHzAUFsZT62v5j+t/8PkFpMB+CX0Fy6lxUKDHvD2Jhj4O9g2gLR78OcYCPiyeMPzFAX2aIcC0mw4uLQu+nivV7U9bHGXISHq4faESEi6oU3carTMf16rUdqf5zaC5pG/0tx8MLTQwfthOfpabR7sO5G/nWPLYH5D+Knrw3OfUkMn7RDDc0XM6zp85S7RCWlUNzdifOfS/Ydf08aEhW81QU8Fvx2/8dTrhgkhhBCifISFhfHWW29Rp04dLCwsdMPkoqKiij6xCBcuXMDAwIBWrR4mnjY2NtSvX58LFy488fz27dsTGhrKnTt32LdvH76+vvj6+hIYGEhWVhaHDh3C19cX0A7nS05OxsbGRjd3y8zMjIiICN0wyUclJiYSGxtLy5YPv+vp6+vTrFmzfMd6e3vnee3g4MDt27eLjN3f358RI0bQuXNnvvnmmwJjKEvS01XJqVQqfBx92HxlM4eiD/GSw0vaHdePaedRpdxhua0jJ4wNMDU05ZsO32Kgl//XrlKpGOwxmNN3TrP92na+DfmWJV2WaOde1esKdTtqy7rv+wYOzNXOr+o5X1sEozBhu+B6MBgYQ9uPnnwzVapCjRbac8IDoPlw7fbcXi7HptqhiI+r1QZMbCD1rvbc3MQqt4iGwyOlSJ2aan/euQgZyWD0yBywS39rf944Bks7QPN3oeO/tXGVkJejJX+eullk0nU8Utu13q6ebf61xUpBu3q2fNytAbO2X2T29ou84u2AhfHz60YXQgghKpoqBlUIHhhcbtcuiV69euHi4sLSpUtxdHQkJycHLy8vMjMzdcUnHh2y+KThgaWhYcOGWFtbs2/fPvbt28dXX32Fvb09s2bN4tixY2RlZel60JKTk3FwcNANR3zUs1ZVfHxYoEqleuKwy+nTpzNw4EC2bt3K33//zeeff87atWt1vWplTXq6/gFednxsXte1IFjxCqTcAbuGrK5WHYDJLSbjbF7I8L4HxjUZh4GeAYduHuJQ9CPzxPQNoMMUbaKl0oOTK7XVCLPSCm5IUWDPl9rnLUcWvxKia2ftzyuPlA/Nnc/1+NDCXHr6D8+7vOPh9twiGg6NHm4ztwcLJ1By8lY2zNHA9aPa57Xba/cfWwpLOxZ+j0XwdNIOFTxXRDGNkAeLIDd3KXlSV1wj29amrq0p8alZLN1/tcyuI4QQQlQGKpUKE0OTcnmUZJj/3bt3uXTpElOnTqVTp064u7sTHx+v2587hC4mJka37dSpvKN01Go1Gk3eed3u7u5kZ2cTHPww8cy9loeHR7Hev7Zt2/Lnn39y/vx52rRpg7e3NxkZGSxZsoTmzZtjaqqdu9+0aVNu3bqFgYEBrq6ueR7VqlXL17alpSV2dnZ56iloNBpOnChgdNITGBoa5rt3gHr16jFx4kR27tzJq6++yvLly0vc9tOSpKsQlaF6Ya6XHF9ChYpL8Ze4Fx+hrQCoyQC3riS/vYE76doelS4uXZ7YlrOFM2/W166d9W3It+Qoj/3VoPlweGOltvfq8t+w/h3QZOdv6MJmuHUG1Obw8sTi30zdTtqfV/c9HCoYeVD706VN4efV66b9GbZT+zNHAzFntM8dH1t0L7e3Kzrk4bbYc5B5Xxvv23/A0L+0vWf3rmrntJWQp6N2eOH1e2kkpGbm25+lyeH0dW1C1qwMky4DfT0+7lYfgGUHIrh9X6oZCiGEEBVd1apVsbGx4ccffyQ8PJw9e/bg7++v2+/q6oqzszPTp08nLCyMrVu3Mm/evDxt1KpVi+TkZAICAoiLiyM1NRU3Nzf69OnDyJEjOXjwIKdPn2bw4ME4OTnRp0+fYsXm6+vLmjVraNy4MWZmZujp6dGuXTtWrVqlm88F0LlzZ3x8fOjbty87d+7k2rVrHDp0iH//+9+FVg388MMPmTlzJn/++SeXLl1i/PjxxMfHl3heeq1atQgICODWrVvEx8eTlpbG2LFjCQwMJDIykqCgII4dO4a7u3uJ2n0WknQVorJULwSwNrbGycwJgCs7P4GkaLCuA68t53rGPd0xZurirYPwvvf7mBuacyn+Eluubsl/gHtPGLRem3hd2gZbJuSd45WjgT1faZ/7jAZTm+LfjGNjbWn3jCTtML/EaG3JepUeOBcwnytX3U7ayoR3LmqPvxsOWSnaiojV6j12jQdJ16PzuqKOaH86t9T2nNVuB14PJrDmDjssAcsqhrjYaIdCnr+Zf5HkCzFJpGVpsDA2oK5t2a5P0c3TnsbOVqRlaVgYEF6m1xJCCCHEs9PT02Pt2rWEhITg5eXFxIkTmTNnjm6/oaEha9as4eLFi3h7ezNr1ixmzJiRp43WrVszatQoBgwYgK2tLbNnzwa0Vf2aNWtGz5498fHxQVEUtm3bVuxKfu3bt0ej0ejmboE2EXt8m0qlYtu2bbRr147hw4dTr1493nzzTSIjI7GzK2BNVmDy5Mm89dZbDBkyBB8fH8zMzOjWrRvGxsbFfOe05s2bx65du3B2dqZJkybo6+tz9+5dhgwZQr169XjjjTfw8/Pjiy++KFG7z0KllLR+5QsmKSkJS0tLEhMTsbAonepyZeGD3R9wMPog0+Lu8npyOry7E2o0Z/u17Xy872Ma2zZmZY+VxW7v/87+H/NPzMfe1J6/+v6FsUEBH/aLW7VDDJUcaDsJOk7VJjJHfoCzv4GxFUw4A8aWJbuZ9e9oKx62naQt4LFxhLbS4nuBRZ+3vAdEBmnX/TK2hD/eA+dW2vfiUVf3wS+9waomTHhQUv63odoy8h2nQruPtdvCA+DXV8HMDvwvlrii4ZhVJ9h6NoYpfg14v33dvKEGRfDFX6F0qG/L8uFFJJOl5PCVu7y19AgGeip2+7enVrWSL8AshBBCVCbp6elERERQu3btEn9pFxVDTk4O7u7uvPHGG3z55ZfP7bpFfXaeNjeQnq5/iFpG2rGx1wwNof0nUKM5AFFJ2go3NS1KtujuIPdB2JnYcSvlFjsjdxZ8UINXoOd/tc8PzIX/NdHOgTr7m3Zbh3+VPOGCh/Ozwnc/MrSwkPlcj9INMdxRcBGNXLnDDROiICVO20uX29NV0+fhcbXagNpMWzQk5mT+dnLl5GjPz0zJszl3XtfZAoppHH8wn6sshxY+yqeuDe3r2ZKdozB356Xnck0hhBBCiJKIjIxk6dKlXL58mbNnz/LBBx8QERHBwIEDyzu0ZyZJ1z9E7ava5OSaeTVtD9EDuUmXi4VLidozNjDmlTraNa+O3SpiiGWzYdBhqvZ5fAQYGHO/YX9WdJrAbL1EPgv6jAl7J/DD6R/Izilg7ldB6nbU/ow59bAwRnGSLrcHSVfEAYh6UHzj0SIauYwtHw45jD6hjTv5FugZgtMjZUkNjMD1wRyzwoYYpt6D1W/AT920vWWP8Howr6ug4YUndEmX9ZPvq5R80l07t2vLmRiu3El+btcVQgghROXg5+eXp7z7o4+vv/66zK+vp6fHihUraNGiBS+//DJnz55l9+7dz3XuVVmRkvH/BLGhuMScBwc7Is2r5SnjHnX/QU+Xecl6ugCa2zXnp3M/ERIbUvSB7SZpqxNmZ6Dx6MOHByYRcnVjnkMCogK4HH+ZWW1nYaj/hDHD5vZg1xBiz8L9GEClXVfsSWzra4cMJkTBzQc9U48X0cjl1Ey7Hlh0CKTGPTi2CRg+Vs61nh+E/gmXtmuHHj4q5ox2eGVCpPZ1+C5tew8SN68Ha3VFxKVwPz0L8wfl2m8mpBGTmI6+nopGzk/RE/iUPB0taVfPlv2X77Dj/C1G+7o+U3vJGdkcCo9j3+U7hMUmU7uaKV5OFng6WeLpaIGRgX4pRS6EEEKI52HZsmWkpRVctdnauuz/UOzs7ExQUFCZX6c8vBBJV79+/QgMDKRTp06sX7++vMMpfWfWUitL24t0IzWWLE2WLrF52uGFAE2qN0FPpcf1+9eJTYnFzrTgSY+oVNBkMABLT/9ASGwIJgYmDGgwAAu1BTlKDj+c/oFdkbvI1GQyz3ceRvpGRV/ctZM26QKw8yreWlkqlba369hS7WuDKlCtfsHHOjaF02u0c9Du39RuKyixc+uqLeIRe1abzFk9eB/PrtcuFJ2dDlYu2sIlV/fCgW/hzVUAWJuqcRc4b9EAACAASURBVLKqQnRCGudvJvFSHW1BkdyhhZ6OFmWyPldRunnasf/yHXaej33qpCs+JZOP158h8NJtsnMeTgk9eu0e6x4UI6pubsS/X3GndyPHElccEkIIIUT5cHJyKu8Q/rFeiOGF48eP55dffinvMMpGjgbO/EZ1jQYTPTUaRcP15OsAJGcmczf9LvB0PV1majMaWDcAeHJvF3Dy9km+P/09AFNfmop/M39GNBzBe97vsajjIoz0jdh3Yx/j9owjLfsJa1/lzusCcGld/KDrdX/43N6r8MWbc4cRRodA5GHt85oFJF2mNtpiHPBwqGN4AGx8T5twuXbRFvjwmwWo4OIWuH1Rd7qn44P1uh6Z15U7tLBpzeczn+tRnd21ifOp6wncTip5+fi7yRm8tfQIuy/Ekp2jUMvGhCE+Lsx9vRFjO7jiW98Wa1M1t+9nMH7tKd788QiXY++X9m0IIYQQxSY140RJlcVn5oVIunx9fTE3Ny/vMMpGxD64H4OqSlVcrOoAcC3xGvBwaGFJysU/rpmdNjk5Hlvwegq5EjMSmbx/MjlKDv/P3nmHR1Wmffg+U9J7r5BAQocQutJUUERBAXXtdWV117aLa/tc236uunbdxbLuKuqHioqgKIqISu8QaggkBNJI720y7fvjzZlMkplkJgUC+97XNdc5c8573vOeGOL85nme3zN3wFzmDpzb6vz5sefz9sy38dZ5s6VgC6/vfr3jG8dPFCYW4LwpsiMSpgibeHBsoqESNULUcNWXQdmxlns6QhVyGauFoPriNrCaIeV6uOFz8AkRqY1DRA0cm1ueTU0x3J/XIrp2nRQ2/qfLRMOeyAAvUuJFF/i16UVuXVtSIwTXkcIawv09+fa+Kfz60IX89coRXD02jj/PGsyS2yew5dGL+PMlg/DSa9ieXc5lb2zksx05vfE4EolEIpE4RbVAr6+vP8MrkZxtqL8zrtrou8IZTy/csGEDL730Ert37+bUqVOsWLGCefPmtRqzePFiXnrpJQoLC0lJSeEf//gHEyb0vs32WcG+z8R2xFUk+GlJLz/CyWpRY6SKLndNNOwZGzmWjw9/3Gmk63+3/S+n6k4R7x/P45MedzhmfNR4Xp7+Mvesu4cVmSu4J/UeAjycWG3qPGDWc5CztXX0qjP0XmL8oa+EAHOGzlMIL7X2K3yoEE+OGHwZ/PSUMOj45Deih1i/82HuG61t5KcuEpGuA18I58agfjZhtWp/AVOSwrh8VDTpp0TkZ1zC6RddAJcMi2RfbiVrDxdx40TXfjeKqxu5/r1tZJXUERngyScLJzntL+al13LvRcnMS43lmVWHWXu4iMdWHECn1XD12LiefBSJRCKRSJyi1WoJCgqiuLgYAB8fH5nyLukQq9VKfX09xcXFBAUFodX2XH36GRdddXV1pKSkcMcdd7BgwYJ255ctW8aiRYt45513mDhxIq+//jqzZs0iIyODiIgIAEaPHo3J1N4Z78cffyQmJsat9RgMBgwGg+19dXV757k+g6EG0leJ/ZTrSSjdAcCJ6hNASz1XvH98l28xNkJEuo5XHaesoYxQ7/aNjvNr81lzYg1aRcuL017EV++8B9TU2KkkBSWRWZnJymMruWX4LR3c/Fbxcpc5r4kaM9UF0RmxY1tEV0dGHWHJomar/LgwzQhOgGv/Twi3tvMlThfRxy3/gMte4vyBodw4sR9Lt+fw8PL9bMssJNBShVdgBNGB3g5v19tcMiySl9ZksCWzjFqDCT/Pzv8MPLx8P1kldUQHevHpwkku9fmKC/bhXzeP5ZlVh1my5QQPf7kPvVbhytEyX1wikUgkp4eoqCgAm/CSSFwhKCjI9rvTU5xx0TV79mxmz57t9Pyrr77KwoULuf322wF45513+O6773j//fd59NFHAUhLS+ux9Tz//POntTt1t0hfBcZ6CBkIsWNJaBJ/UNT0QjXi1Z1IV5BXkE0k7Snew8X9L2435nDZYQAGBQ9iRNiIDudTFIUbht7AX7f+lU+PfMqNQ29Eq+lhlzvvoBar946IGdOy76ieS0VRRLRr6z/BM1CkFPq2F58ATH1QiK49H8H0R1B8w3h23gi89Vr+vSmbcYee41Wvnzmkmwj5Qa0t6k8TSRF+JIT6cKKsnvUZJVw+KrrD8dmldfyaUYKiwMe/neBWY2VFUXhq7jAMJguf7shh0ef78NRpuHREx/eUSCQSiaQnUBSF6OhoIiIiMBqNZ3o5krMAvV7foxEulTMuujqiqamJ3bt389hjj9mOaTQaZs6cydatW3vlno899hiLFi2yva+uriY+vuuRol5l36dim3I9KAoJgQlAS6Qrt0YYanTFRMOecZHjyKzMZHfRboeiK70sHcBmutEZlydezmu7XyOvNo9N+ZuYHj+9W+vrMvaCpyPRBXD+faIn19jbRP2WMxKnid5gp/aJVMOxt6EoCo9fPhR/nZkrtwob1OF120Uj6cGXwcxnIHxQ95/HRRRF4ZLhUfxrw3HWHi7sVHQt3SbE+wWDwkmKcL82UlEU/jZvBE0mC8v35HH/Z2l8/4C/0/REiUQikUh6Gq1W2ysfpCUSV+nTRhqlpaWYzWYiI1tblUdGRlJYWOjyPDNnzuSaa65h9erVxMXFdSjYPD09CQgI4OOPP2bSpEnMmOFCxORMUJkraowARv0GaIlolTeWU2WoskW6umIXb8/YqGYzjULHZhpHyoVbn6uiy0fvw1XJVwHwyZFPurW2bhE+GMbcChPvhqBOhLV/FMx/G/o5MdtQURQY0mwicmyt3WGFBwaV46sYqNIEYRj+G2FFn7Fa9Po6zVw8TPyb+vlIMUazxem4hiYzX+zOA+Dm87oeMdVoFF68ehRTk8NoMll4YuVB6SYlkUgkEonkv4Y+Lbp6ip9++omSkhLq6+vJy8vjvPM6b7R7zz33cPjwYXbu3HkaVtgFDq0ArNB/CgSLD8O+el8ivEWd2+Gyw5Q3Cpe8noh0ARytOEqVoardeVV0DQ11vVv4tYOvRUFhS8EWjlcdd3tNJ6pOsPr4agxmQ+eDnaEocMWbzXbvPUhyczQw6xcw2a0vU4iwwFGX43nNe7DwZ3G87FjrcaeBMf2CCfX1oLrRxI7scqfjVu0roKrBSHyIN9MHRXTrnlqNwt/mjcRTp2FLVhkr9uZ3az6JRCKRSCSSs4U+LbrCwsLQarUUFbW2ti4qKurx4ra2LF68mGHDhjF+/PhevU+XydkmtoNbO/upKYYb8jYA3bOLVwnzDiMhIAErVtKKW9fPlTaUUtJQgoLC4OAO0u7aEOcfxwXxFwDwafqnLl9ntBh5b/97LPhmAY9sfIQrV17J99nf962oSXQK+EWBsQ5Obmk5nrlObNV6s+jRwhbfaoGKE6d1iVqNwoyhQkStPezYOt5qtfLRthMA3DixP1pN9x2f+oX6cP+MZACe/S6dirqmbs8pkUgkEolE0tfp06LLw8ODsWPHsm7dOtsxi8XCunXrXIpWdYc+HemyWiG/OdUvrrUoTAhIAFpEV3dMNOxx1q9LjXL1D+iPj9ofy0VuGHoDAN9kfUO9sfMeGhnlGdz43Y28ufdNjBYjPjof8mvzeXjDw9y4+kbbWs44igLJzc2dj/0otlV5UHxYpBQOuLBlXOhAsV+W2fGcDRWwdyk09VyvkfMHhgFw+JRjh859eVUczK/GQ6fhN+N6rq5x4dQBDIr0o7yuiRe+7yP/zSQSiUQikUh6kTMuumpra0lLS7M5EGZnZ5OWlkZOjrA7X7RoEe+99x4ffvgh6enp/P73v6eurs7mZthb9OlIV1Uu1BaBRieiKnaoIkvt0dUdu3h7bKKr0LHocrWey56JUROJ8I6g3lTP0YqjHY49WnGU67+7nvTydAI8AnhuynP8eu2v3Dv6Xrx13hwoPcDda+92SbydFpJnia0qujJ/EtvYca37gYWooivL+VymJlj6G/j6D7DptR5bYoC38NFpaDI7PP/xVlETOGdkNCG+Hj12Xw+dhufmjwRg2a5cdp5wnt4okUgkEolEci5wxkXXrl27SE1NJTU1FRAiKzU1lSeffBKAa6+9lpdffpknn3yS0aNHk5aWxg8//NDOXKOn6dORrrzmNUWNBH3rXk9qeqFKT0W6JkSJZtSHyg5RUl9iO+6uc6E9iqKQGJgItIhEZyw/uhyjxUhqRCpfz/uauQPn4q3z5q6Uu1i9YDWxfrGUNZaxNH2p2+voFQZcIERxWaYQVKroSprZelxokth2FOn66SnIEz3YOPSViHT2AN56Ibrqm9r3uKuoa2LV/gKgewYazhiXEMJ148UXAot/6STKJ5FIJBKJRHKWc8ZF1wUXXIDVam33WrJkiW3Mvffey8mTJzEYDGzfvp2JEztxkOsB+nSkK89xaiFAYkBiq/fddS5UifSNZFT4KKxYWZfTku5pM9EIcd1Ew9H6VKdFR5gsJn448QMAd468kzDvsFbnw7zDuDf1XgA+OPiBQ7OP045XQIsN/ZHv4Ph6sZ/sTHQ5iXQdWgnb3hL7qogrTu+RJfp4COtcR5GuA/lVNJksJIT6MDo+qEfu15a7poso34ajJRRXN/bKPSQSiUQikUj6AmdcdPVV+nakq1l0xY5rdyrGLwadpqX9WnedC+25uJ9w5Vt7Urjw1TbV2iJUQ0Ldj3SBXTpktfNI147CHZQ3lhPkGcR5MY5r+S5LvIzk4GRqjDW8f/D9Lq2lxxnUnGK45U0wVINPKESnth6j1nSVOxBdZVnwtRCTTH4AkppdEQ9/3SPLU0VXvbG96KoziOhXmJ8nitJ9Aw1HJIb5MrZ/MBYrrEyTToYSiUQikUjOXaToOtswGUTjXYC49qJLq9G2Elo9Kbpm9hdRml1FuyhvLCejIgOACJ8IQrxCOrrUKer6Oop0rT6+GoBL+l+CXqN3OEajaLg/9X4APkn/pFUK5Bkj+RKxrWtey8AZoGnzTy5kgNjWnAJDbctxswk+vxWaaqDf+XDRkzDsSnEu/ZseWZ63KrocRLrUY+qY3uKqMXEAfLk7r285UEokEolEIpH0IFJ0OaHPphcWHgSzAbxDWj6wt0F1MOwJu3h74vzjGBY6DIvVws85P9tSC4eFDOvynPbGH44+dBvMBls642UDLutwrulx00kJT6HR3Mi7+9/t8pp6jLBBEGRXD9W2nguEqYZPqNi3j3YV7IWiA+AZAFe/D1qdaA+g0QkXxNIO6qBW3A3/mQW1xR0uz8dDRESbTBbMltY/ezX65euha3ddT3L5qGg8dRqOFtVyMN+xi6KrNJksrD1cxKLP0/jzF/t469dM1hwqJKesj5irSCQSiUQi+a9Fii4n9Nn0QtVEI268sBx3gGqm0VMmGvZc3L8lxdBmotHF1EIQQk6jaKgz1lHWWNbu/Ma8jdQaa4n0iSQ1ItXBDC0oisIDYx4AhPFGbk1ul9fVIyhKS7QLpaU/V1scORjmNvdhS5gCAdFi3zsYEqeL/XQnKYYlR2Hfp+L6/7sKGp0LGR+7KFZbM4365vRCn16OdAV667lkuOi5t3xPXpfmyC2v58mvDzLxuZ9Y+NEuvtqTz5e783jxhwzu+ng30176hfs+3Uthlawbk0gkEolEcmaQoutsw0l/LnvGR4lzqs17T6KKru2nttt6dnXFuVDFQ+tBtK8QFY7qulZni9TCyxIvQ6N0/us6Pmo8E6MmYrKaWHdyXafj7fkh+wdu/f5Wlh9d3nOpbmpKYP/zwTfM8RhHZhq528U2fkKb+a4Q28NOUgwPr2zZL9wPn90ARsdiw1Onsen2tmYapyu9EOCqMbEAfJ2WT5PJ4ta1BZUNXPX2Fj7aepKKeiPh/p7cOSWRRRcPYt7oGEbGBqJRYNW+Ama88ivvrs9y+x4SiUQikUgk3aV3c4fOYhYvXszixYsxmx33MDpj2CJdzgXVlNgp/HzNz+1c/nqC/gH9GRQ8iKMVR8mvFeYHXXUuVOnn34/82nxOVp9kTOQY2/HaplrW5wrXv85SC+2ZED2B7YXbSS93zeWvydzESztf4rOMzwDYU7yHtSfX8vT5TxPlG+XGkzggcSrcscZpKijQ3kzDaoUcVXRNaj12yBz49k9wKg0qTkBwQuvzqsnGxLtFM+UTG+GrO+GaD0HTWkApioKPXktdk5kGY1vRJSJdvp69/ydianI4kQGeFFUb+PlIMZeOcO1nXmswcceSnRTXGEiO8OMvc4YxeWAoOm1rcX4wv4onvz7InpxKnv/+CKsPFrL0zon4nYZnk0gkEolEIgEZ6XJKn0wvrC0RH7RRILbjKFa4T3ivuc6p0S6AAI8AW6Sqq6i28W17df2c+zNNliYSAxMZHDzY5flUEajWnHVEQW0Bt35/q01wXdL/Ejy1nmwu2Mz8r+ezKmuVy/d1Sr9J4Bfh/LwqutReXRUnoK4YNHqIGd16rG8Y9J8s9tPbrK00E4oOirqv6Y/AdUtB6yHGbXjJ4a29PdReXU4iXfrej3RpNQrzUkW0y9UUQ5PZwr2f7OFIYQ1hfp58cPt4pg8Kbye4AEbEBvLl3efz0tWjCPLRsy+3krs+3oXB1Me+UJFIJBKJRHLOIkXX2YSaWhg+GLwCz9gyLul/iW1/aMjQbos7tfasrYOhfWqhO/cYGipEV3ZVNvVG5yYKjaZGbvn+Fg6WHSTAI4DFMxbzygWv8MXcLxgVPopaYy2Pb3qc45XH3X0k92jbIFlNLYwZ3a75NdCSstg2xfDwCrFNnC4MOgZMh8tfEcfSljpsquzjxMFQTTf09ex90QVwdbOL4S9HiqmqN3Y41mq18tdvD/NrRgleeg3/uXUcccE+HV6j0ShcMy6ej+6YgK+Hls2ZZSxatq+dgYhEIpFIJBJJbyBF19mErSlye6v408mAoAEMDBTRme7Uc6k46tXVaGpk5ykRZbQXea4Q5h1GmHcYVqwcrTjqdNzuot0U1RcR6hXKF3O/YFrcNAASAxP56NKPmBI7BStWPjnyibuP5B5q6mFDBdSX29VzOWkCPmQOoEDeDsj6ueX4oebUwuHzWo6NuAp0XlCZI6JgbbA1SG40wKEVsOM9sFioa04v9O5l90KV5Eh/4oK9MVmsZBTVdDh2U2YpH209iaLA69eOJsWN5s2j4oJ49+Zx6LUK3x04xdPfHJJW9RKJRCKRSHodKbrOJtR6LgdNkU83d6fcTbx/PHMHzu32XGqvLnvb+L3Fe2myNBHhE0FiYKLbc7qSYrgpfxMA0+OnE+MX0+qcVqPl9uG3A/BN1jdUN3XPzrxDPHzBv/n+ZVl29VxORFdANExYKPa/uV84FJZlCYt5RdssyuzmHniR2D+yut1UobpG7tR+x9ivL4QvboPVf4ZDX9kiXz6nIb1QJTHMF4ATpXUdjvt23ykArhsfz6Uj3E9tnZIcxmvXjkZR4ONtJ/l0xxl2uZRIJBKJRHLOI0WXE/pcny6LGfL3iP0OnAtPF5cmXsrqBasZHOJ6rZUzYv1j0SpaGkwNlDSIRsLbTwnhMSl6UpfSF9UIXEdmGlsKtgBwfsz5Ds+PjxpPUlASDaYGVh5b6XBMj6HWdRXsFX24wLnoApjxlOgBVpULa59scS1MnCZSC+0Z3GxCkvFd6+PFR3in/A7+ol+Kd30BqO6QB5fbRNfpSi+EFtGVXeZcdJnMFtamFwEwd1SM03GdMWdUDA/PEr8jr67NoNZg6uQKiUQikUgkkq4jRZcT+pyRRmUOWIyg94WI7rkF9jX0Gr0t0qTWdW07JfpUTYqe5PS6jlDrutReYm0prCvkeNVxNIrG6T0UReGGoTcA8OmRTzFbetF4Qa3r2vcpYBWuhP6Rzsd7+sGVi8X+7g9g29ti3z61UGXQpYACp/ZBpV1U55dn8bfUcNwSxfaRz8CdzRb7x9aiaawCTl96IUBCaOeRrl0nKyivayLIR8+ExBCn41zhzqmJJIb5UlrbxL/WZ3V+gUQikUgkEkkXkaLrbCEkER7Lg7s2tLP+PhewORhW51BlqOJwmYj2TIzuINrTAWp6YWZlJkZze2OGzfmbARgZNpJAT+emJJcnXk6ARwB5tXlszN/YpbW4hC3S1RzNbGsV74jEqTC+Oc2wrqQ5tdBBuqdfuHBQBMj4XmyL023uh78zLuJg5JUQOwbCh4LFyNgG8fPxddSnq64U3p4M39zn6tO5hC3S1YHo+uFgIQAzh0Y6dCp0B71WwyOXikjtexuzKaqWzZMlEolEIpH0DlJ0nU1o9RCWdKZX0Sv09292MKw5ya7CXVixkhiYSIRPB1brHRDrF4u/hz9Gi5GsqvZRjM0FQlRMjp3c4Tw+eh+uSr4KgKXpS91eh8Fs4HjlcQxmQ8cDQ9v8d23bFNkZM58WaYYgRJhvqONxbVMMN74KwMGA6WRa42hoNs5gxAIAphuFwHTYHHnDS8KUY8/Hwvijh0hQa7rK6rA4cBW0Wq38eEiIrlnDu9k/rZlZw6MY2z+YBqOZV390broikUgkEolE0h2k6JL0CewjXWpq4cSorkW5QKQGqtGutimGJouJbQXiHpNjOhZdANcOuRaNomHbqW1kVXaehrbt1DYW/bqIuSvmMnHpRK78+koW/rgQo6UDK/S2oqufi2mVnn5wzQeQMBWmP+p83JDLxfbEJlE3dvBLALbE3ArYWcYPF6JrvGU/IVTj0za9sOIE7PxP8xsrHP/FtXW6QFywN1qNQqPRQlFN+6jTgfwqCqoa8fHQMjW5Zxp/K4rC/1wmaru+2J1LRmHHzokSiUQikUgkXUGKLkmfwL5X1/bCZhONmK7Vc6k4M9M4WHqQGmMNgZ6BDA8d3uk8sX6xXBh/IQBfHv2yw7EGs4GH1z/M2pNrOVF9ArNViJm9xXt5O+1t5xcG9W8xsvAMgHA3rPhjx8Jt30L/85yPCR0o5rSYYNktYLVA0kyqgsXz20RXWBLW6BR0ioXZ2h3t0wt/eU7UFtJsbpL5Mz2FXqshPlj0JXOUYqimFl4wOByvHnRVHNs/hNkjorBY4YXvnRuvSCQSiUQikXQVKbqc0OfcC89x1PTCE1UnyK7KRqNoGB/VvZ+9Krra2sarVvHnRZ+H1sX6uOlx0wE4XtVxo+Tvs7+nwlBBlG8U7858l3XXrOPl6S8D8O8D/2ZnoRNjFp1HS5pg3PjeqdtTUwyrmvuhTXvIFslqsGuObBo6H4C52q2t0wsLD8L+z8X+jCfENutnh02XbVTmwprHoabQpSXaUgxL2ze1XtPDqYX2PHzpEBQFfskoIb+yocfnl0gkEolE8t+NFF1O6HPuhec40X7R6BQdJquoLRoWMowAj4BuzTksdBggRJfFarEd78wq3tn6AE7VnXI6xmq18km6aKR83eDrOD/2fCJ8IpiVMIsFyQuwYuWxjY9RZahyPEFYsth2ZBXfHdQUQ4D+U6DfJLybI0b1xhbRVZd0BQATlCP4GEparln3V8AKw+bBpD+Ipss1BVDivBca39wLW/9pqyHrDJuDYRvb+MziGrJK6tBrFS4c0rU6v45IDPNlTL9gAH5utqSXSCQSiUQi6Smk6JL0CXQaHXH+cbb3XXUttCchIAEvrRcNpgabFX1lYyUHSw8CboouXyG6CusKbQ2c25JWkkZ6eTqeWk+b+YbKI+MfISEggaL6Ip7a8pTjOaY9DCnXtzQ+7mlixkBgv+Z7/RkAn+ZIls1IA6jxima3JRmNYkW79R+iqfK2t+HYGuGQOONJ0HtD/+Z6uCwnKYY52+H4r837W1xaojMHwzWHhBCanBRGgJfepbncZcZQIeZ+Si/u8hwWi5V16UW89Wsmj311gJv/s52b/7OdL3fn0WjsxZYDEolEIpFI+jRdasJTUFDApk2bKC4uxmKxtDp3//3398jCJP999Avox4nqE0DPiC6tRsug4EHsL93PkfIjJAYmsvXUVqxYSQ5OJtK3gz5YbYj0EWMbTA1UGaoI8gpqN0aNcl0+4PJ25330Prww7QVuWn0T63LWsaVgS3vnxPjx4tVbaDRw03KozoOBokZNTR+st0svbDCaWWU+j7GaY7DtLfFSGXtri7190gzIWgeZ6+C8e9rfb8OLLfuFB6GxCryc2/ODfXphW9HVe6mFKhcPjeTFHzLYmlVGncGEr6d7fx5rGo38aVmaQ9G28Vgpf111iAVj4rhzaiJxwT49tWyJRCKRSCRnAW6LriVLlnDXXXfh4eFBaGgoiqLYzimKIkWXpMv08xdRGA+NB6kRqT0y59DQoewv3U9acRq5Nbn8+8C/AddcC+3x0nkR4hVCeWM5p+pOtRNVRXVFrD25FoAbhtzgcI7hocO5YuAVfHXsK7YWbO3Urr5XCB8kXs2oNV32oqvOYOIr81Qu90xjfJhZRLX03uAfBRf+pWWugReJ7cnNYGwQY1TydkPmTyIy5h0M9aWQuxOSZ3a4vMTm9MKT5fVYLFY0GoWSGgP780RKphqN6g2SIvzoF+JDTnk9G4+VcukI1wXeybI67vxwF8eKa/HQabh8ZDTxIT7EBXtTUmPgs5055JY3sGTLCb7ZV8BHd0xgRGzHAlQikUgkEsm5g9ui64knnuDJJ5/kscceQ6Pp+9mJubm53HzzzRQXF6PT6XjiiSe45pprzvSyJA5IChK26WMix+Cl8+qROVUzjU+OfGI7lhKewu0jbnd7rmjfaJvoGho6tNW5z49+jtlqZkzEGAaHDHY6x7jIcXx17Cv2FO9x+/69QUt6oV2kq8lMNb78j9+zrP3DdOcXhw8B/xhR15WztUWEQUuUK+U6YbSx7xMxphPRFRPkhV6r0GSyUFDVQFywDxuPibqy4TEBRPj3zO+FIxRFYcbQCD7YfIJ16UUui66tWWXc/X+7qWowEhngyb9uHkdKfGtR/vvpA9mUWcrffzjCoYJqrn9vG0tuH8/Y/iG98SgSiUQikUj6GG6rpvr6eq677rqzQnAB6HQ6Xn/9dQ4fPsyPP/7IH//4JbuSAwAAIABJREFUR+rq2ttRS848cwfO5YExD/CXSX/pfLCLqGYaAFG+Ubw47UU+nv0xIV7uf9hV67rammkYzAablfyNQ2/scI6xkWMB0Tus3tjeoc8RVquVpelLuWbVNfyS03N9scAuvdDYUtOlRr18HDVGtkdRWoRW5rqW46f2wdEfhAX+1Adbeo7lbOt4vsZqdPUlxIeI1DvVwXD9USG6pg8Kd+WRusXMoSKN9JeMYocNmttSZzDx+6VCcI2OD2LVvVPaCS4AjUZh2qBwPv3dJMYnBFPTaOKmf+9g07HSHn8GiUQikUgkfQ+3ldNvf/tbvvjii95YS68QHR3N6NGjAYiKiiIsLIzy8vIzvCqJIzy0Htw58k5bz66eYGjIUH436nf8aeyf+GbeN8xOnN0qJdYdonxF5KOwrrX9+ca8jZQ3lhPpE8lF/S5ydKmNGL8YonyjMFlN7CvZ1+k964x1PLThIV7Y8QJHyo+w6NdFrDmxpkvrd4SjSFdds6lGu8bIjkhqft6sZjHYVA8/Pyv2R1wt6r/6NfcPy98FpibH81QXwFuT4B9jGR0oGiNnl9VhtljZ0Cy6Lhjce6mFKuMTQvD31FFa20RaXmWn45ftzKWy3khimC+f/W4SEQEdR+ICvPR8dMdEpiaH0WA0c8eSnex34T4SiUQikUjObtwWXc8//zzr16/nggsu4L777mPRokWtXu6yYcMG5s6dS0xMDIqisHLlynZjFi9eTEJCAl5eXkycOJEdO3a4fR+A3bt3YzabiY+P79L1krMPRVG4L/U+7hhxB946784v6ABnkS61D9iU2CnoNJ0LlTERYwA6TTHMqszi+u+uZ82JNegUHWMixmCymnh4w8N8e/zbrjxCO3z07Wu6GlyNdAEMuBBQoPgQLF8ILyfDsR/FsWaHRMKSwTsETI0iCtaWpnr49DqozoemGmZqRJuGE6V1HMivoqLeiL+njtR+7SNIPY2HTsO0wSKitq4T63ij2cJ/NmUDsHDqAJcbNnt7aPn3reO4aEgETWYLf1l5ELMLUTWJRCKRSCRnL10SXWvWrKGoqIgDBw6wd+9e2ystLc3tBdTV1ZGSksLixYsdnl+2bBmLFi3iqaeeYs+ePaSkpDBr1iyKi1scwkaPHs2IESPavQoKCmxjysvLueWWW/jXv/7l9holEnDeq0ttmJwYmOjSPGqK4Z4i56KrpqmG2364jeyqbCJ8Ivjg0g94f9b7zE+aj8Vq4X82/g9fZ37dlcdohZpe2GA022zsbemFrrj3+YRATLPpyYHPoalWNHm+cjGEN9e2KUpLtCtna+vrLRZYcVcrMZZaJ5pXnyit49cM8e98SnIYeu3pSWme2WzWsa4T6/jVB06RX9lAmJ8HC8bEunUPT52Wv181Cn9PHfvzqli2M7fL65VIJBKJRNL3cdtI45VXXuH999/ntttu65EFzJ49m9mzZzs9/+qrr7Jw4UJuv10YH7zzzjt89913vP/++zz66KMAnYo9g8HAvHnzePTRRzn//I57MxkMBgwGg+19dXW1q48iOcex9eqqbZ1emF0loh3uiq59Jfswmo3ote37Tu0t3kuloZJIn0iWzVlGqHcoAE+f/zR6jZ7Pj37OM1uf4YL4Cwj07LoLnhrNslqh0WjB20NLvZpe6GLkhskPiJTChMkw6jpRw9U2hbPfJMj4ToiuyXYOp78+B+nfgEYPc9+Ar/9AVPlOAqklu8yX8nqRjng66rlULhgUgUaBI4U15FXUO7R3t1qtvLteiO1bz0twOcplT7i/J3+6eBB//fYwL645wuwRUQT7enR7/RKJRCKRSPoebn917OnpyeTJp8fquqmpid27dzNzZovjmUajYebMmWzdurWDK1uwWq3cdtttXHTRRdx8882djn/++ecJDAy0vWQqokRFrekqaSjBaDECYLKYbI2XBwQOcGmeAYEDCPIMwmA2cKjskMMxacXii4RJ0ZNsggtAo2j4y6S/MDBwIEaLkc35m7v8PADedmJBFVtqpMvblfRCgOHz4L5dQjT1P6+94ALo3/xlR842Ed0COPAlbHhJ7F/xJqTeCBHDUKxmZmj2kFNWz75cUe80ffDpE13Bvh6MSxBGK86iXZsySzl8qhpvvZabz+t6DeIt5/VnSJQ/lfVGXlyT0eV5JBKJRCKR9G3cFl0PPPAA//jHP3pjLe0oLS3FbDYTGdm6iW1kZCSFhYVOrmrN5s2bWbZsGStXrmT06NGMHj2aAwcOOB3/2GOPUVVVxcsvv8zgwYNJSkrq1jNIzh1CvELw0HhgxUpxvfgwXlBbgNFixFPrSYxfjEvzKIrSaV3X/pL9AKREpDi8fnq8sHLfkL/B7eewR6NR8NSJPwOq2FK3vp7uR2+cEjUKdN7QUA5lx+DUfvj6XnFu8gMwurm32ZA5AMzW7cZksWKxwuBIf6ID7erx6svh+0dazDt6gQnNoiuzuNbh+X9tEFGua8fHE+TT9eiUTqvhr1eOAOCznTnSVEMikUgkknMUt0XXjh07+PDDDxkwYABz585lwYIFrV59jSlTpmCxWEhLS7O9Ro4c6XS8p6cnAQEBPPjggxw5coTdu3efxtVK+jIaRWOLdp2qFXVdaj1XQkACGsX1f05jIptFl4O6LpPFxP7SZtEV3l50AUyLmwbApvxNmC1mh2NcxceurgtaIl4uuRe6is4D4saJ/SPfwbIbwdQASTNhxlMt44YK0TVVsw8vRJrvBfZRLmODMN3Y/g58fQ9089mdoab5VTYY2507XFDNxmOlaDUKv53iWkppR0xIDGF+aixWKzz7bXq355NIJBKJRNL3cFt0BQUFsWDBAqZPn05YWFirVLzAwK7XljgiLCwMrVZLUVFrF7GioiKiolxrXNpVFi9ezLBhwxg/fnyv3kdydtHWwVAVXa6mFqrYzDSK92CxWlqdy6zMpMHUgK/el4GBAx1enxKeQoBHAFWGKptAc4X9JftZlbWq1T1VcdU20uWSe6E7qP261v0VKnMgOBGu+jdo7O4TNQqC+uFFE9M14rls9VwWMyy/E3K3i/fV+ZD5U8+usZkgb1FnV+VAdKl9wy4aEmHrKdZdHrl0CBoFdpwoJ7fctf5tEolEIpFIzh7c+irbarXyzDPPEB4ejrd39+y3XcHDw4OxY8eybt065s2bB4DFYmHdunXce++9vXrve+65h3vuuYfq6uoeF5OSs5e2vbpsJhpB7kU8hoQMwVvnTU1TDccqjjE4ZLDt3L5i4eQ3KmwUWo1j4aPT6JgcM5nvT3zPhrwNpEakdnrPX3J+YdGvizBZTWzM38jfJv8NvVbf0iC5TU1Xr4kurKD3hes+Ae/g1mMUBYbMhW2LuUS7k426SYxNCBZOH6v/DEe+Ba2nqB07/ivs/hAGzXJ+T6tViDWte1G7IJ9m0VXfvq9YeZ2IwCWE9ozgAogK9GJCYgjbjpfz/cFT/G6aY7EtkUgkEonk7MStSJfVaiUpKYm8vLweW0Btba0t7Q8gOzubtLQ0cnJyAFi0aBHvvfceH374Ienp6fz+97+nrq7O5mbYW8hIl8QRbW3j3bWLV9FpdIwOF02729Z1qU2THdVz2TMtXqQYbsjrvK5rQ94GFq0Xggvg++zvue/n+6g31rdrkKyKL++eTC8EiJsgBBPAvLcgcpjjcc0phjM1e5gxOARPQwWsfgh2vQ8oIjo2+0Ux9ugPUH3K8TwAP/8v/C0K8jvuidYWVXQ5Si+srDc2j+lZp8HLR4rfre8OuFavKpFIJBKJ5OzBLdGl0WhITk6mrKysxxawa9cuUlNTSU0V39QvWrSI1NRUnnzySQCuvfZaXn75ZZ588klGjx5NWloaP/zwQztzjZ7mnnvu4fDhw+zcubNX7yM5u7BPL7RarbZIl7vphdBS17W7qHXdYFqJ+ALCWT2XypSYKWgUDUcrjtoib47YmLeRP/7yR0wWE5f0v4R/XvRPvHXebC7YzMK1C/HQNwIOjDR6OtLlFQA3fgE3fCEcD50RPxGrTxiBSj2vWl6G10bAzvfEuctegmFXiB5g/c4DqxnS/s/xPOXZsPkNsBjh0Aq3lhro3VzTVd9edFU0HwvuYdE1a0QUigL7civJq+h6iuHhgmqW787j7z8c4c4Pd/GnZWnsOlFu68MmkUgkEonk9ON2TdcLL7zAQw89xMGDB3tkARdccAFWq7Xda8mSJbYx9957LydPnsRgMLB9+3YmTpzYI/eWSNzFPr2wrLGMmqYaNIqG/gHu24aPixTGElsKtlDbJFzyyhrKyK0RjXJHhY/q8PogryBGhYkxzqJdGeUZ/PGXP2K0GLm4/8W8MO0FpsdP571L3iPQM5D9Jfsp9lwK2Ee63LSMd4cB02HQJR2P0WhRhlwGgD5rjTDciBkD138GExa2jBt7m9ju+ajFht6eDS+BRUTtyN3h1jIDm2u6qhuNmC2txUplc8phsE/7/mrdIcLfy+aa+H0Xol1mi5XHvtrPZW9u5MEv9vH2r1n8lF7Eir35XP3OVua/tYVv9xe0ex6JRCKRSCS9j9ui65ZbbmHHjh2kpKTg7e1NSEhIq9e5gkwvlDhCjXQV1BZwvFKkFsb6xeKpps25QWpEKomBidQ01fBZxmdAi1X8wMCBBHgEdDqH6mLoTHSty1lHk6WJ8VHj+fu0v6PXCKGQEp7CPy4SrR+qlP2gGG1phQ22SFcPpxe6w/iF4BsOidPhlq9h4c8wuE0T9WFXglegMOU43sY+viwL9n3a8r5gL5gMuIoquqxWqGlsHe2qaBZdPZ1eCHD5KDXFsIOUSQc0mSw88NlePt2Ri0aBiYkh3DSpH0/PHcZ14+Px0GlIy63k3k/28oeluzGZHYhUiUQikUgkvYbbn6pef/313lhHn0MaaUgcoUa66k31NtfArqQWAmg1Wn436nc8tvExPjz0ITcMucHlei6VaXHTeHPvm2w/tZ1GUyNeOq9W57MqswCYHjfdJrhURoePJsI7guKGYrQ+J6g3in5RdTbL+F6IdLlK9Ch4KLPjMXpvGHUd7HgXdi+BpBkt5359AawWSJ4F+bugvkz0Bot37UsUD50GXw8tdU1mKuuNrQRWS01Xz0a6AC4dEcVT3xwiLbeS/MoGYoM6NyxqNJr5w9I9/HykGL1W4Y3rUrmsuT5M5cFLBvPxtpO8sz6LNYeKeGT5AV66ehQajYNG1hKJRCKRSHoct0XXrbfe2hvr6HMsXryYxYsXYzb3Th8gydmJt86bYM9gKgwVbM7fDHRddAFcmnAp7+x7h5PVJ1mWsczlei6VQcGDiPSJpKi+iJ2FO5kaN7XV+Y6MPhRFYXLsZFZkrkDnm0FDk4gk9Wp6YU8z9lYhujJWQ8YPkHwJlB6FA1+I8xc9LgRYxmphNd+R6KouAI0e/IRFfZCPB3VNDa3MNKxWq+19T9d0gUgxHJ8Qwo7scr4/cIo7p3b8u2W1Wln40S42HivFU6fhnZvHcuHgiHbjwv09WXTxIEbGBnL3/+1m+Z48Arx1PDlnGIoihZdEIpFIJL2N2+mFAGazmeXLl/Pss8/y7LPPsmLFinNOnEgjDYkz1GhXWrEQSO46F9qj0+hYOFLUKS05tIRDpYcAbM6GnaEoii3FcEvBllbnTBYTJ6pPADAwyLEF+ZTYKQBo/TKobzJjMltoMonUs47SC/eV7LM1iD6jRA6H/lNE7dan18JbE+HrPwBWGDIHolMgfoIYq/b3ckT6KnhjNLw71dZwWU0xrLSzja8xmGw1Ub0R6QJ7F8POf77bjpez8VgpXnoNH90xwaHgsufiYZG8dLWoA/xg8wneXNdJNFEikUgkEkmP4LboyszMZOjQodxyyy189dVXfPXVV9x0000MHz6crKys3lijRNKnUOu6VPv17ogugMsGXEacXxzljeU0mhvx9/AnITDB5evVHl2Hyw63Op5Xk4fJYsJb521bc1smxUxCQYPWs4TSxkLqjS1fnjiKdBktRp7b/hw3rb6Jq1ddTW51rsvr7DV+8xGcdy94BogoV36zG+SF/yO28c3GO7nbRZFWW3Yvgc9vAbMBak6JpsvY9eqyi3RV1ol9b70WL33vRAJnN7sY7s2ppKCyocOxn+0UrTXmp8YycUCoS/MvGBPHU3OFXf9rPx1l+/Gec6OVSCQSiUTiGLdF1/3338/AgQPJzc1lz5497Nmzh5ycHBITE7n//vt7Y40SSZ9C7dWl0l3RpdfoWTiqxZVvVPgoNIrr/zSHhgwF4Ej5ESzWFoOErCrxJUhCQILT+QI8Aoj2HAJAvmGPzURDo4CnrvU1FY0V3LX2Lj49Igwqqpuquf+X+6kz1rm81l7BNxRm/Q3+dAhmPQ9RI2HqgyIKBhCTChod1BYJ0w0VqxXWvwSrHhD1XzSn2ZWJn5utV5edbXyLiUbvRLkAIgK8GNdfNI1ef7TE6bjK+ia+PyhcDq8b38+te9w+OZHrJ8QD8NKaDGknL5FIJBJJL+O26Fq/fj0vvvhiK6fC0NBQXnjhBdavX9+jizuTSPdCiTPso0ahXqEEenbfaGXugLnE+MYArtdzqSQEJuCp9aTeVE9OdYuosPUQC+q4LijJX1jXF5v2UWcQ0TtfD12rWp/jVce5/rvr2Vm4Ex+dD0+f9zTh3uFkVmby+KbHW4m9M4ZXAJz3B7h7E8x4suW43lukGUJr6/gtb8Ivz4r9aQ+JejCAclEH56hXV286F9qTHOkPwKmqRqdjVuzNp8lkYWh0AKPi3P8d/OPMQXjqNOw6WcGvGc7FnUQikUgkku7jtujy9PSkpqam3fHa2lo8PHr3g8jpRNZ0SZyh1nRB54LGVfRaPX+b8jdmJcziN4N+49a1Oo2OwcGDARHtUlEt7QcGOq7nUhkWJL5YqLKmU9Uo0tnapha+susV8mvzifePZ+llS7lq0FW8duFr6DV61uWs493977q15tOOfYohQG0JrH9R7F/8v3DRXyC0+efULLpska6GJti3DLb8g+o68fPp6R5dbQn3Ey0ISmoc29xbrVY+2yFSO6+fEN8lM4zIAC9uOz8BENEui+zfJZFIJBJJr+G26JozZw6/+93v2L59u62R8bZt27j77ru54ooremONEkmfwj7SlRjQvdRCe8ZFjePl6S8T6u1abY49Q0JEiuDh8pa6LjW9sDN3xQEBg7CY/LEoBvY1uyf6erY20ThYKpqhvzD1BZKCkwARkXti0hMAvJX2FrsKd7m97tNGWzONDS9BU61IPTzvXnEspPnnpIquZiON+toaYc7x418Ys/n3+FPfK86F9oT7dyy60nIrySiqwVOn4cqU2C7f5+7pA/Hz1HH4VDWrD/YBYxSJRCKRSM5R3BZdb775JgMHDuS8887Dy8sLLy8vJk+eTFJSEm+88UZvrFEi6VPYi66einR1lyGhQnQdKRORLovVYksvTAzqWBj6eOox1w4CYG/pVkAYRaiUNpRS3liORtGQHJzc6tr5yfO5LPEyQDRi7rPENYuuooNQeBB2vS/ez3wGNM1/BkOaf05tIl2+1ZnCHRGIK9vMlx5Pk6jt3XQ8m+iqdSy61CjX5SOjCexG1C3Y14OFzbb0r/54VDZNlkgkEomkl3BbdAUFBfH111+TkZHBl19+yZdffklGRgYrVqw4p5oIy5ouiTNCvUPRaUQkqLsmGj3FsBDhRpdeno7VaqWwrpAGUwM6jY54//gOr/Xx0GKqFemJhyp22I6pHK04CkA//35469o361V7g+0v2d/9B+ktAmMhMF4YZnx+C1iMMHAGDJjeMiZETS/MBovFVtMVUtfsyhqaTLUulMGaPH6feZdottxLqKKr1EGkq9ZgYtX+AgCum+CegYYjfjs1kRBfD46X1rF8T16355NIJBKJRNKeLvXpAkhOTmbu3LnMnTuXpKSknlxTn0DWdEmcoVE0TI2dSoR3BCPDRp7p5QCQFJyEVtFSaaikqL7I1hS5v39/9JqOIyHeei2muiSwKhQ1nkTRVeJjl154rOIYIBoxO2JUmOj7lF6eTpO5yeGYPoGaYljeLKJmPt36fGC8cDk0G6A63xbpimxoHp80g5f7vc1BSwK+pgr46aleW6p9TVdbZ8Fv9xVQ32RmQLgv4xOCu30vP08dd08X0a6l23M6GS2RSCQSiaQrOO9+6gSz2cySJUtYt24dxcXFWCyt01F+/vnnHlucRNJXeePCNzBbzbaI15nGU+vJgKABHKs4RnpZOjk14sOzK+mPPh5asPiAoR94nUTrm4WPfojtvBrpcia64v3jCfIMotJQSUZ5BiPDnQvR0oZSthZs5UDpAQ6VHiK3JpeHJzzMnAFz3HncrhE/EQ4uF/sjfwPRo1qf1+ogOAHKMqH8OEE+ov9ZvEmkaRIxjBOngrnPeB+/eD4Ix9dDfTn4tDi5UpIBn14n5r/gUeiCwQW0RLqazBaqG022Rs0AO7LLAbgiJaZLBhqOmDc6ludWH+FAfhXldU2E+HatZq3OYCItt5JAbz2xQd4E+eh7bI0SiUQikZzNuP2J8YEHHmDJkiVcfvnljBgxQv4PVfJfiaIo6JS+IbhUhoYMFaKrPJ3i+mKgcxMNAB8P8RzGukT0XifR+mTj49mSXphRngE4F12KojAibASb8jexv3S/U9HVZG7i6m+upqyxdTPeV3a9wsx+M/HSeXX+kN2h33liq9HDRY87HhMyoFl0ZREUKhwPEy05ooVX5HAq6xvJtkZTEzQE/8ojcORbGHNLy/Wb3xQ1YetfAKwtDZrdxEuvxd9LR02jiZIaQyvRVVAlHBQTQn27NLcjIgK8GBLlz5HCGjZllnJFSozbc/xypJjHVxygwM7m3luvZdqgMJ6bP5LQ5uidRCKRSCT/jbj9qfGzzz7j888/57LLLuuN9Ugkki4yNGQo32R9Q3p5OlWGKgAGBnVsFw8t9vDG+v7oQ0HrfdJW02W0GG0uiINCHIsuECmGm/I3caD0gNMxe4v3UtZYhp/ej3lJ8xgRNoI397xJQV0By48t58ahN7r8rF0iehTMeQ38Y0REyxF2DoZBPnqCqCFSqRTHwgdTUS/SjasHzMF/zxE4tLJFdDVWwaGvWuZa/3fQecHURV1abri/p010JUX42Y6rvbtigtrX13WHaYPCOVJYw4ajJW6JrvK6Jv666hAr00SdWaivB4qiUFproMFoZs2hIg7kVbH4xjGk9ut+OqREIpFIJGcjbtd0eXh4nJM1XBLJ2c7Q0KEApJelk1Xpml08tJhmmOv7A6D1LEGjqwfgRNUJTBYTvnpfW/NmR4wKF6l6B0qci67NBZsBuKjfRTwy4REuH3A5vx35WwDeP/A+BrNjp74eZdwdMPhS5+ftzDS89FpG6oWxhCmgH3j6U1knGiWbhza3xzj+q0gxBDjwBRjrIWywcEUEWPcMbH3L8b3KsmD3h2Bx7Bhoq+uyczC0Wq020RUd2LORwanJYQBsPFbSro7MGSU1Bma/sYGVaQVoFLhzSiIbH7mQXX+ZyZH/vZQVfzifAWG+FFQ18pt3t/Lx1hMuzy2RSCQSybmE26LrwQcf5I033jjn/8cp3QslZxtqg+Si+iKqm6pRUOgf0L/T6/RaDXqtAhYfvK2i51O1VdRx2ddzdZRKPCJsBAA5NTlUNlY6HLM5X4iuyTGTbcfmJc0j0ieS4oZivjr2lcPrTitqpKtMiNYUvYje1AcPxmi2UGMQ1vF+MUMhciRYzSLFEISAAhh7G0z5I1zwmHi/5jHHTocr7oZV97eOjtnhqFdXWV0TTSYLigJRPSy6xieE4KnTUFRt4FhxrUvXvPVrJkXVBvqH+vDVHybzlznDbOmqXnotqf2C+freyVw6PAqj2coTXx/iXxuO9+i6JRKJRCI5G3BbdG3atImlS5cycOBA5s6dy4IFC1q9zhWke6HkbMPPw49+/i0W4nH+cS7XSal9uXRGITrKTKLfV2cmGiqBnoEkBCQAsL+0vcAori/maMVRFBTOiznPdtxD68GdI+8E4D8H/nPm3Q9Dm0VXhbCNH6oTka4q/ySqGkSUS1EQNVbDrxRjD62Egr1QuB+0HpBynTg+/REYNFvsq8JMpa4U8pr/thxd43ApjkTXqUoR5Qr380Sv7bL5rEO89FomDhCNuTcc7bwPWUFlA0u3CcOWv80byej4IIfj/L30vH3TGB68WPwOvfLjUY4V1fTQqiUSiUQiOTvoUp+u+fPnM336dMLCwggMDGz1kkgkZw41xRBcSy1UUaMTproEAIqa0gHXRRdgs893VNe1pWALAMNDhxPs1bquZ37yfCK8IyiqL2Jl5kqX19wrBPYTtvGmRqg5RZJViIoS7yQq64UgDPDSo9UoMGy+uOb4r7DpNbE/7MoWN0NFgaFzxf6xH1vfJ+tnwNqy7yDF0JHoUk00onu4nktlWnOK4YZjpZ2O/ecvmTSZLUxIDGFyUmiHYxVF4d6LkrhwcDhNZgt//nK/bMQskUgkkv8q3DbS+OCDD3pjHRKJpAcYEjKENSdE5MQVu3gVta6rqjIOj2Aoasyi3ljvnugKH8mq46sc1nXZUgtjJ7c756n15I6Rd/DCjhf494F/Mz95foe9xQrrCnli8xOMDBvJ71N+j17bcR8yt9DqIKifcCAsy6Sf6SQABZ6JmOtFpEvt30VYkkgxLDoAh78Wx8bc2nq+pJliW7AXaovBL0K8P7a2ZUx9qZgjOqXVpY5quk5VCtEV08OphSrTBoXDd+lsP15Go9GMl17rcFxueT2f78wF4MGLO049VVEUhecXjOLi19azL7eSf2/K5u7pnRu9SCQSiURyLtCz+SkSieSMMjSka5Eu1cHQ0BiIxRiIBQsb8zfarOeTgjo3z1GbJB8oPdCq5tNsMbP11FbAsegCuCr5Knz1vpyqO0V2VXaH93ll1ytsO7WN9w68xy3f30JeTV7nD+gOqplG9ga8rfU0WbXkKjFU1IlIV5CPXQ8rNcVQvS7ch7fAAAAgAElEQVRhSuu5/CMherTYz1wnthYLZDXv+0W1PmeHw/RCm4lG70S6kiP8iArwwmCysPNEudNxb6w7hsliZWpymC0l0RWiAr14Ys4wAF5de5TMYplmKJFIJJL/DqTokkjOIYaEtDQ1HhjoehRBjXQBmOsTAViWsQyAWL9Y/Dz8HF5nz6DgQXhoPKhuquZk9Unb8UNlh6gyVOGv97elILbFS+dFjJ9wRyypd15PtK9kHz+c+AEFBX8Pfw6WHeQ3q37Djyd+dHqN26hmGs11WFnWGCoMUNkc6Qr2sYusqSmGAGNvddwMOfkSsVVTDE/thfoy8PCHyQ+IY1ntm8qrostQXQqr/ghb37L1wIoJ6p1Il6IoNhdDZ3VdWSW1fLVHCN0HLxns9j2uGRvHBYPDaTJZeOjL/ee8KZNEIpFIJPBfILoqKysZN24co0ePZsSIEbz33ntnekkSSa8R6h3KjH4zGB46nMEhrn8g9vZoyTQ21ycAsLNQGD24kloIoNfqbTVl9nVdamrhpJhJ6DTOM5ojvEXqnRpda4vVauWVXa8AcMXAK1g+dzkp4SnUGGt4cP2DHdrVu4UqukqazUSs8VTWN1HZICJdwfaRrrAkGHy5SEkcfZPj+ZIvFtusdWA2tUS1BkyHQbPEfs42MLR2DAz382S4ks2Hpodg9wew9glKKqqB3ot0QXOKIbDRSV3Xu+uzsFhh5tAIp+YZHSHSDEfi46Flb04lu05WdGu9EolEIpGcDZzzosvf358NGzaQlpbG9u3bee655ygrKzvTy5JIeo3XL3ydz+Z8hofWo/PBzfjY1e6YGxJanXNVdEFLv659Jftsx9T+XPZW8Y4I9xEf9ksaHEdY1uWsY2/xXry0XtyXeh/RftF8cOkHTIkVKX0/57aPFnWJ0NYRwgxLPJX1Rira1nSpXP8J/PEA+DpJs4sdC97Bonly3k7I/EkcT75YCLyg/mAxwolNrZdxdBlfeTxNvNL887CY0FaeACC6lyJdAFOSwlAUOFJYQ3F1Y7vzB/OF8Lt2fL9251wlOtCby0ZGA9iiZhKJRCKRnMu4Lbo++ugjDIb2TUybmpr46KOPemRRPYlWq8XHxwcAg8GA1WqV6SwSSRvs0wsthgh8df62926Jrua6rh2FO8isyKTKUGWLejmr51IJ9xaiy1Gky2g28tpu4RB46/BbifSNBECv0TMrQUSLtp/a7vI6OySkdS3cEWs8lQ1Gm3thkLfrYhYAjbbFUGP/shar+IEzRDpi0gzxPsuurmvdX9F+ez+eipG15jE0NvdgC6oTPa5i7CNdJzbDyS3urakDgn09GBoVAMDe3PY91/IqROPs/qE+3brPgjGiJ9y3+07RaDR3ay6JRCKRSPo6bouu22+/naqqqnbHa2pquP32291ewIYNG5g7dy4xMTEoisLKle0toxcvXkxCQgJeXl5MnDiRHTt2uHWPyspKUlJSiIuL46GHHiIsLMztdUok5zLeHvYudRpGhLY46bkjulLCxXXZVdnM/2Y+s5fPxmK1MDBwIFG+UR1eG+Ej0gsd1XQty1hGTk0OoV6h3DHijlbnJkVPAkTtWE1TDxgzBPUDpeXncdQaT1W9kYq65pou3y64Jap1XXs+AqsFwodAULw4NrBZdKlph2mfwkaRRrnE6yZ+Z1xEZdBwAAaQh06j2Oq9aKiEj+fDkjlQfMT9dTkhMcwXEC6F9lQ3GqluFA2iY7tpWz8pMZTYIG9qDCZ+PFzUrbkkEolEIunruC26rFarQ3vgvLy8LvXpqqurIyUlhcWLFzs8v2zZMhYtWsRTTz3Fnj17SElJYdasWRQXt3wbrtZrtX0VFBQAorfYvn37yM7O5pNPPqGoyPn/4A0GA9XV1a1eEsm5jo9Ha2vwMZGpAHhpvYj3j3d5nmi/aJ6f+jyTYybjqfWkxihE0LS4aZ1e21F6oWrqcU/qPfjoW0dYonyj6B/QH4vVwq7CXS6v1SlavRBegFnvR541jKoGIxX1DtwLXWXgDEABa3NER418ASROEyKvPAsOfAmr7hfHp/6ZdeG3YEVDsVcCAMmafCIDvESfMIDCA2A2iHnXPtGFh3VMXIgQVHkVDa2O5ze/D/LR4+vpdseRVmg0CvNTRbSrOymGlfVNHCuq4WB+FbtPlktHRIlEIpH0SVz+v2ZqaiqKoqAoCjNmzECnsyu8N5vJzs7m0ksvdXsBs2fPZvbs2U7Pv/rqqyxcuNAWRXvnnXf47rvveP/993n00UcBSEtLc+lekZGRpKSksHHjRq6++mqHY55//nmeeeYZN59CIjm7sTfSALio33TeO/A2E6MnotU47tXkjDkD5jBnwBwaTY3sKdpDdnU2Vw68stPrnBlpmC1mmy381NipDq+dEDWBk9Un2V64nQv7Xej0HlarlazKLLae2srWgq3k1uTy/NTnGRE2ovXAkAFQkY0pdAjUKFQ2NBHUICJcwW1rulzBNxTixrWkFtqLLq8AiJ8AOVth+Z2AVZhzXPg44V/uByBPG88oIEkpINq+R1fh/pb9Yz9C1i8w0Pnzu0p8sBC2bSNdquiKC+4ZI48FY2L55y+ZbDhaQnF1IxEB7tWqfb4zl8dXHsBobp0yPm90DE/NHU6wbxcEskQikUgkvYDLomvevHnA/7N33uFR1dn/f90p6b1XktAJJaEXaQoIqIhtRXdd18Yqa1lFf351XbF31rK7rIW1rbprQ7EhFqR3EkILJUAC6SG9lym/Pz5zpySTMslABD6v55nn3rn13BjJvOec8z5C4MyePRs/P5uFtIeHB4mJiVx99dVuDa65uZm0tDQefvhh6zaNRsPMmTPZunVrl65RXFyMj48P/v7+VFVVsWHDBhYtWtTu8Q8//DCLFy+2vq+uriY+vuvf9EskZyP2mS5PnYbBoYP45spvCPJ03Z1OxUvnxaTYSUyKndSl49VMV2lDKSazCY0iEvGnGk5hMBvQKTpr31drxkeP57Mjn3XY19VgaOB3q35HVkWWw/bX0l9j+cWtXE1D+8OxNShRyZADjS0miiymEsHdyXSBKDHM2wl6H0ho9TPpN0OILswQkQxXvQkajbWM8Bhx4jClgJhAu/sXWkSXV6Aw6vjxUbh9vegj6wHxIRbRVdFKdFmGM/e0tFClb7gfo/oEkX6ykq8yClg4teuz5d7dnM0T32QCEOitx1uvxUOnIa+inpUZBWw6WsoTlw/jkuFRXRreLJFIJBLJ6aTLouuxxx4DIDExkQULFuDldfrcs1RKS0sxGo1ERkY6bI+MjOTQoa71L5w4cYI//vGPVgONu+++m+HDnc8KAvD09MTT05Nly5axbNkyjEbZ4C0597EXXWrZWJx/3BmNIdQ7FAUFo9lIeWM5Yd6i9zK/Nh8QZYTtZd3GRY0D4GjlUUobSq3n2pNenE5WRRY6jY5xUeMYGTGSN/a8wbbCbWRVZDEgeIDt4LG3QX0Z+kl/QrsjG6PJbJ3TFejdjUwXwPDfwLbXYcS1oPN03DdoLqx9RrgcXv8/8BRGJuF+4ris5hAMigeeNDPEy85iXc10zX4OVj8Mxftgz8cw8nfOY6g9BT4hnYqyeEsmK7e8waGkXDXRiAvumYmGPVeNiiP9ZCUr0vO4bUpSlwTSsrVHeemHwwDcNjmJRy4dYj0vI7eSBz/fw5HiWu78bzq/Hd+HZ64YJoWXRCKRSHoVl3u6/vCHP+Dl5UVzczN5eXmcPHnS4fVrY9y4cWRkZLBnzx727t3L7bff3qXz7rzzTjIzM9m5c+dpjlAi6X287Szj7dfPJHqNnhCvEMDRTKOgVvRmxvrFtntusFewdTD0jkLnRjsZp0QZ8iVJl/DmrDe5I+UOZvQRJhYfHvzQ8eDwgXDN2ygRQwhqJbK6XbIWkgT/lw1zX2i7L2oY3Pw93L4BghNtYVgyXSW1LRTqRcZ9gEaIUFoa4JQQHvSdDlPvF+u/PAXNjhkqQPSLLR0Aa5/tNNTYYG8UBRpajJTVNVu3uzvTBTBvRAweWg2HimrILOy8h9ZecP15xgAHwQWQGh/EN3dP5p4ZA9Ao8N/tJ/kiPd9t8UokEolE0h1cFl1ZWVlMmTIFb29vEhISSEpKIikpicTERJKSktwaXFhYGFqtto3xRXFxMVFRHTuh9ZRly5aRnJzM2LFjT+t9JJJfAz52PV2+nr0jusDOwbChreiK9ovu8Fw127WjqB3RVSJEl+qwCPD75N8D8O2xbylrcD6/L9Cuh0uvVfD1OE0/n4SJNkdDC6roOlXTRLYiMo/xxlyxsyRTGGj4hEJADIy7XRiA1BTCplccr91cBz/+FTDD7g/BZOowFE+dlkh/Uc1g39elGmvEuqmnC8TPd2ay+O/+9Z6CDo+tazLwj19Eeej/zRnMfbMGOs1geeq0LJ41kMWzhPPmo1/tJ7u0zm0xSyQSiUTiKi6LrptuugmNRsO3335LWloa6enppKens3v3btLT090anIeHB6NHj2bNGtv8GpPJxJo1a5g4caJb79UamemSnE/Ylxe2NtU4k1gdDO0zXXXig3iMX0yH546PHg/AtsJtbfYZTUb2nhKleKkRqdbtKeEpDA8bTrOpmU+PfOr0uvaZriAfjzNaphZhJ7oyW4TojGjMETvVfq6oEWLel94LZj0ltm16WTgbqmz9lxBjALVFULC703vHWxwMc+0cDN1tpKEyqZ8oB80qru3wuJ8PFtPYYiIh1Ic7pnXe/7Voen8m9A2hvtnIPf/bTbOhY7EpkUgkEsnpwmXRlZGRwZtvvsncuXNJTU0lJSXF4eUqtbW1ZGRkWB0Is7OzycjIsJYqLl68mOXLl/P+++9z8OBBFi1aRF1dXbdmgrmCzHRJzifs53T59FJ5IdgNSG6wORh2pbwQYEzkGHSKjvzafKvboUpWZRb1hnr89H70C+xn3a4oCjcMuQGATw59QrOxmdbYW8QH++gxm80crzyOyXz6P8CH+4lsU3WjgT1NIrvvVyMGJFv7uaJH2E5Ing9D5oHJACsXgbEFaktg86tiv78lW3jo207v3drBsKHZVmoYF+S+ni6wM+4od1IWacfXGeJ34fKUmC6JX61G4dUFIwny0bMvv4qlPx7uebASiUQikXQDl0VXcnIypaWlbgtg165djBw5kpEjxVygxYsXM3LkSJYsWQLAggULWLp0KUuWLCE1NZWMjAxWr17dxlzD3chMl+R8wr6P61dRXuikpyvat+PyQh+9D8PDhUlO6xJDtbRwRPiINmYcsxJnEeETQVljGd9nf9/muvbGGUHeHvxt19+Y/9V8Hlj/AGazuc3x7iTAW4eHVvwznWUSmT5deRaYzbZMVpSd6FIUuPRlYchRtE+UGa57DpprIWYUzHpSHHd4Vaf3jrMIIdU8I79SLP09dQR4uzcbqhp35FU0tPszrahrZv0R8XsxP7XjrKc9UYFevHi1+Bm9teE4u3LKexitRCKRSCSu47LoeuGFF3jwwQdZt24dZWVlPR4kPH36dKuzoP3rvffesx5z1113ceLECZqamti+fTvjx493+T6uIjNdkvOJX2t5oclsorBOlMV1lukCW19X6xJD1UQjNTy1zTl6jZ7rB18PwEcHP2qz3150NXtv5/3M9wH46cRPfJH1Racx9QRFUax9XSfMURjQojTXQFUuFB8QB9mLLgC/CJj7klhf/yKkiXi5+GlhW6/RwalDUHbM8TyzGRoqhFg7vJpRRiHqcstFSaF9P5e7SyztjTtKa9tmGwG+31+EwWRmSHQA/SP8Xbr+xUOjuGa06Il7d0tOT8OVSCQSicRlXBZdM2fOZNu2bcyYMYOIiAiCg4MJDg4mKCiI4ODg0xFjryAzXZLzCfvywtNmFNEFrAOSLeWFpQ2ltJha0CpaaxasIybGiF7PjXkbqW+xlapZTTQinJdAX9FfzCE8WH6QJmOTw74gi5GGxusk2QgBMyxUDFN+YecL5FTldOnZukuYRXS1oKNYZ8nwHFoFLfVi5ldov7YnDb9GDFg2tQizjUGXQuIF4B0EiZMt1/jOdnzRPnhtBLyQCG9Mhv8tYPq2W0hVjlpndamiKzmgEQ6vFiLNTTgYd1Q4LzH8eo9wILw8petZLntuviARgB8PFFFe51zYSSQSiURyunBZdK1du5a1a9fyyy+/OLzUbRKJ5OzD3r3QuxdFV+tMl1paGOkTiU7TeQZuZMRIEgISqG2p5Ztj31ivlV+bj4LCiLARTs8L9rR9YVTX4uhyF+StR9FV4R3/ASYMzOgzgw8u+YDxUeNpMDTw0MaHaDG1uP6wXUSd1QVQ5m1xiN1nMf2IHOZ85paiwGUvg3cIaD1h1hO2fYMvE0u1xLClEVYshErLyA+fUPAMBGC05ggFlQ0YTWarXfxtVf+E/y1wFG1uwGrc4aSvq6iqke3ZoixwXkrHZabtMTQmkOGxgbQYzXyRntf5CRKJRCKRuBGXRde0adM6fJ0ryPJCyfmEfXmhT29muizZrLLGMgwmg3UwcmfOhSoaRWMtFfzvof9iNpvZc2oPAAOCB+Dn4ef0PK1Gi49O9DDVNbcSXT4eeMV8jEZXQ4i+D89OfhadRsfTk58mwCOAA2UHeD3jddcftouo5YUAdQGWrFZ+mlhGOxeRAPhHwR2b4E9bIcxu8POguWJ5cpsYlrz2GTh1EHzD4f4j8OBxmPgnAJK1ubQYzRRVN1qcC80k1VsMPHI2uukJBapxR56dW6LKt3sLMJthdEJwjwYzXzdOWPJ/vDP3tPfjSSQSiURij8uiC2Djxo3ccMMNTJo0ifx88aHogw8+YNOmTW4NrjeR5YWS8wlPnQa1TcenF3u6gj2D0SpaTGYT5Y3l1n6uroougPn95uOj8+F41XG2FW6zlhY66+eyx08vBFlti6Ntua8X6HyzAfhN/F/w0YsP/VG+USyZKAx//r3v3xTVFXU5RlcI97O5JxpDBzrubN3P1ZrA2Lblh4FxEJ0CmGHNE7DlH2L7vL+Dv8WgKHIoAMN0YiZYbnk9eRX1RFCJd0uFOEYVfm4irgMHw2/22FwLe8LlKTF467UcLakl/WRFj64lkUgkEokruCy6VqxYwezZs/H29iY9PZ2mJtH/UFVVxbPPPuv2ACUSyelHURSrVXxvZrq0Gi2h3qGArSwQumaioeLn4cfl/S4HRLbLaqIR0bHoUsVUa9Hlqbf1/yQFJTrsm504m/5B/TFj5kjFkU5jc2ZJ3xn2mS6P6CGOOzvKdHWEWmK4+wPADCm/hcGX2PZbRFeSKRctRnLL68mvbCBZk2M7pnCvsKR3E6qDYeuerpzSOvbkVaFR4JLh3SstVPH30nPpCHGNj3fkuny+yWRm+Ybj3Pb+Lm59bye3vLeTP/5nF78cKu5RXBKJRCI593FZdD399NO88cYbLF++HL3e5up1wQUXuH04cm8iywsl5xuqa2Fvii6wM9OoL+myXXxrrh8iSgzX567nQKlw+etMdKmZrtY9XTqL6DKbPAjz9WpzXlKg6LM6UX2iw+sfLj/M9E+nc9Pqmyhv7Lptub3oCohLBiwpSUUL4UOcn9QZg+wEVkAczH3ecX9QIuh98aCFRKWI46V1lNQ0kazYPaOxyeag6AZss7ocywt/OSRMVSb2C3X4WXSX6y0lht/uLaSmseuiscVo4v7P9vDMqoP8fLCYNYdK+OVQCT9mFnPLe7t4aMVeapsMPY5PIpFIJOcmLouuw4cPM3Xq1DbbAwMDqaysdEtQvwZkeaHkfEMVW71ZXgh2ZhoNp7o8GLk1fQP7MilmEmbMGMwGQr1CifOL6/AcXw9foG2mS6NtBMBs9CTY16PNeQkBCUDnouuNPW9Q01xDWnEav/vud112PbQXGtGhIRCcYNkxGPRtRWCXiBwKEcmgaGD+P8Er0HG/RgMRQtANVnLZkV2O2QwjdK2e0Y0lhn0soks17lDZl18FwNjEELfcZ1SfYPpH+NHQYuRrS9liZzQ0G7n9gzS+3J2PVqOweNZAXrh6OC9ePYKbJiWiKKJPbO5rG9gp54BJJBKJxAkui66oqCiOHj3aZvumTZvo27evW4KSSCRnHl9PnWXZy5kui5lGcX1xt3q6VH47+LfW9dSI1E5nS1kzXa2MNNCIEmqzyYswv7aZFlV05VTntHvt7Kps1pxcAwgnxrzaPG74/gbSizuvDogL9kFRIMTXQwwlDhskdnS3tBCEu+GNX8GirdDvQufHWEoMB2tOsidXfKE2TGNxOIwdI5YFreIvzoRvF4vSQxeJDPBCr1UwmMwUVtmyXaroGh4b2N6pLqEoCteNFdmuT3d2XmJY3djCje9s55dDJXjqNCy/cTT3zBjAgrF9uHZsPI9fPpT/LZxAbJA3ueUNXP/WNuvPSyKRSCQSFZdF18KFC/nzn//M9u3bURSFgoICPvroIx544AEWLVp0OmKUSCRngJsnJTJ9UDjjkkJ7NY5wb5HpOlR+iCZjExpFQ6RvpMvXmRI3hXh/8eG6MxMNAF+9yHTVGRxFV71BZL7iA0MI6SDTdbL6ZLvXfu/Ae5gxMz1+Op9c9gnDw4ZT1VTFwh8XcrzqeIdxRQZ48eYNo1l+4xghHAdfKnYkX9HpM3WIXwREDO7gxmIW2WDlJAaTGV8aiDMLEczoP4hlfivR9e19sOttWH4RbP47mExdDkerUYgNUm3jheiqbzZw7JT4+btLdIGtN2x/QTUtxo5j/OcvR9mZU4G/l44PbxvPRYPb/i5O6BvK6nuncOGgcAwmMw98tocmg9Ft8UokEonk7Mdl0fXQQw/x29/+lhkzZlBbW8vUqVO57bbbuP3227n77rtPR4wSieQMcO3YeN67eRx+nr1bXqhmulSr9wifCPQafUenOEWjaHj6gqe5asBVXD3w6k6Pt7oXNjuWF6o9XgnBzsvbVNFVWFdIo6Gxzf7iumK+PvY1ALcOu5VQ71Denv02I8JH0GxqZn3u+k5ju3hoFKMTLLPERt0IjxTDoDmdntcjLJmuIZbs1mDFIir9Y2DAxWL91CFosvy8KnMhd5tYN7XAT4/Cfy6HqnZmYplMbQYsW/u6LGYamQXVmM0Q4e9JREA3SymdEB3ohbdei9FkduqWaAvRbHVOfPHqER2WOPp76fnbtamE+XmQVVLLaz9nuS1eiUQikZz9uCy6FEXhkUceoby8nP3797Nt2zZOnTrFU089dTri6zWkkYZE0juoPV1VTaKsLMa3+zbhoyJH8cSkJ/D38O/0WGumq5WRRk1zDUC7M76CPYOt18+taVuu9uHBDzGYDIyKGGU18/DWeXNhvCjryyzL7OLTWFCU7vdyuUJkMgBxSin+1JOssfRzRY8QM8ACYsFsgkIhjtm/QiwTp8Dl/wC9r5jl9e4lYGjl2mhsgbemweuTHPapM7jyLELI3aWFKoqikBAq7pVTVtfucbtzKymsasTPU8eFgyM6vW6IrwdPXyEyhG+sPybLDCUSiURipVtzugA8PDxITk5m3Lhx+Pk5/zByNiONNCSS3kEtL1TpTj9Xd1BFVWsjDfW9mglrjaIoJPg7N9Ooaqri08OfAnDr8Fsd9iWHClFzoMx9DoBuxTtYOBsCg5STNufCqOFiGTtKLFUzjX2fi+Wwq0U27o6N4BsBlSfg8CrHax/6For2QkkmnNxi3RwfotrGi/JCVXQNc7PoAkgMFSI7u7T9TNd3e0U55cwhEXjpu9brOGdYNPNSYjCZ4YHP9tDYIssMJRKJRAJdqiO66qqreO+99wgICOCqq67q8NgvvvjCLYFJJJLzE7W8UOWMia52LOOtoqudTBdAQmAC+8v2tzHT+OTwJ9Qb6hkQPIApsVMc9g0NFeV7uTW5VDVVEejpXFg0G5v5f+v/HyaziUWpi6xi7YwQmQzVeQzW5DJUndGliq6YUXDwG2GmceowFO8DjR6S54v9of2E+Nq4FNLehaF2PWg737atZ/0EfacDEB/sOCB5/2nKdAEkhgnRdaKdTJfJZOb7/UJ0XTrCtd/BJy4fytZjpWSV1PL6umPcN2tg5ydJJBKJ5JymS5muwMBAq/NXYGBghy+JRCLpCUGeQeg0tu+DXLWL7y5qeWGbTJelx8tf336JYntmGl9mfQnAzUNvbuOeGOgZaLWxP1h+sN1rb8zbyC+5v7Aubx0Lvl3AgxseJK+mnT4pd2Pp6xqmZDNIsdzTmukaLZb5abYsV/8Z4GPX9zT6D4ACx9dB2TGx7dQRUXaocuQH66p9T1d9s4GjJRYTjTj3/21JChP3yi51Lrp251ZYSwunDAhz6dohvh48epkQxx/vPInJZO7kDIlEIpGc63Qp0/Xuu+86XZdIJBJ3oygKEd4RFNQJA4Mznulqdp7pUkWZM5yVFxbWFpJXm4dW0XJRn4ucnjc0bCh5tXkcKD3AhOgJTo9ZnbMaEOIzvzaf77O/5+cTP/P27LcZGTGyi0/XTSwOhhdrd+GptGD28EcJShT7YlIBBSpPQvp/xLZh1zieH9QH+s+Eoz9B2ntw8VMi6wWQMBlOboWyLCg/DiF9iQ8W5YXF1U1k5FZiMos5ZZFuNNFQUcsL2+vp+m5vEQCzkiO7XFpoz5xhUfh56iiubmJ3bgWjE9wzZ0wikUgkZyfd7umSSCSS04VqpgE9M9JwhU4zXR2YcSQEtp3Vtat4FyB6t9oTbJ31ddW31LM+T7gbLp22lE8v+5QR4SNoMbXw+ZHPO3uknmPJdIUo4megRA0Tg5NBDFQOGyDWa4tA5w2D5ra9xpibxTLjI2ioFEuAyfdCn4liPesncR9fD3w8tGgw8eM+IbpPR2khQJKlvDC/ooFmg6NtvH1poWov7yqeOi0zh4hS2VX7inoQqUQikUjOBbqU6Ro5cmSng0VV0tM7H/Z5NrBs2TKWLVuG0SiboCWSM41qpqGgEOUbdUbuqfZstdfT1ZVMV3ljOTXNNfh7+FtF15jIMe2ep/Z1tedguCF/Aw2GBuL84iLslmsAACAASURBVBgaOhRFUbhjxB38ac2fyCjJ6OKT9YDQ/pi1HihGi8OgWlqoEjsaSo+I9cGXgKeTvrcBs4XNfE0BrLgNGqtEBqzfDGGkcWITZP0I428XpiRBnjxd+VcGZeQRrJuLNvL0jCIJ9/fE10NLXbORk+X19I+wxa6WFvp3o7TQnrnDo1mZUcD3+wr566VDuvx3VCKRSCR2NFSK/uGk6bYv/s5CuhT5FVdcwfz585k/fz6zZ8/m2LFjeHp6Mn36dKZPn46XlxfHjh1j9uzZpzveM4Z0L5RIeg810xXuE46Htu1A4tNBu5muLhhp+Hn4EeolhkqrfV27iiyiK6p90TUkdAgA+bX5VDa2tRf/IVv0O81OnG39wJ4SkYKCwsmak5Q2lHb+YD1Bq0cJH2R770x0qbQuLbReQycMNUCUGQKMvln84VTnfWVvhGZhnnGD/mdGa7Lwo4E/677gj7uvhE2vQEvbGWg9QdjGW0oMW/V1qaWFM7tZWqgybWA4vh5aCqoa2ZNX5fL59c0GXlx9iLmvbeT2D3bx9zVZrDlYTG2TodsxSSQSyVnHno/hgyvhk9/1diQ9okuZrscee8y6ftttt3HPPfe0mcv12GOPkZvbdkaNRCKRuIrqYHimSgvB1tPVYGjAaDKi1YgP210x0gBhplHWWMaJ6hOE+4RzsuYkGkXTYd9VgEcAffz7cLLmJJllmUyKnWTdV9dSx8Z8YTgxJ2mOwzn9gvpxtPIoGSUZzEyY2b0H7iqRw6Bon1iPGuG4L368WHoHCxON9hh1I2x4Ucz10uhh5O/F9vDBEBgPVbmQvQHix3FlpegP+5/hQsZqDtO/uQB+flz0fV3+D8frGppgy99F1ky1sHeBpDBfMgurHfq6TCYzq/b1rLRQxUuv5aIhkXyzp4BV+wpJjQ/q0nlms5mfMot54ptM8iuFff7Bwmp+OFAMQGSAJx/dNp7+EZ3Pn5NIJJKzGrMZdr0j1vs5748+W3A5R/fZZ59x4403ttl+ww03sGLFCrcEJZFIzm9SwlMAGB05upMj3Yd9+WCdwfYh3Fpe6NF+eSHYHAxPVJ+wZrkGBQ/qdDCzWmLYuq9rbe5amoxNJAYkMih4kMM+VcjtLtnd4bX/b8P/MX/lfN4/8L51yLPLWPq60OiESLInegRc8w78bgXoPNu/RmCsKDMEYSnvZ+nZUxRbtivrR1j/Ij7Gag6Z4vmr4RZ+q38V86Uvi/17Poa6Msfrbn8Tfnkavr2vW4/mbEDywaJqiqob8fXQ9qi0UOWSYaI8dtW+Qszmzl0MmwxG7vgwjT9+kEZ+ZQOxQd68ePUI/nrpEK4cGUtUgBfF1U0seHMbBwurexyfRCKR/Ko5sQVKD4PeF0Ys6O1oeoTLosvb25vNmze32b5582a8vNzvMCWRSM4/xkaNZcOCDfx51J/P2D09tB54aEQpo+pgaDabrT1eXcl0gTDTUPu5xkaN7fS+Q8Oc93U5Ky1UUUVXR31dJ6pPsCp7FcerjrN011JmfT6LF3e+aM3cdZk4yzNEp4Leyb/xw66GuC6I47kvwPg74OKnHberoitzJexcDsDThhswomVoXDDK2FshOgWMzbDnv7bzTEbYIY6naB80ufhc2GZ15dgNSN58VJRsju8b2qPSQpXpgyLw1mvJq2hgf37nIumzXXn8cKAYvVbhT9P78dPiqVw7Np7bpvTllQWprPrzFIbGBFBW18z1y7exN69tWapEIpGcM6hZruHXgFdA78bSQ1wWXffeey+LFi3innvu4cMPP+TDDz/k7rvv5s477+S++7r3beOZoL6+noSEBB544IHeDkUikXSBYK/gM248oPZtqdmtekM9JrPJYV97JAYkAqKnqysmGirOHAyrm6vZVLAJgDmJc9qco4quzPJMGgwNTq+7IW+DNa6+gX2pa6njg8wPWLpraacxOdBnAlz/CVy93LXzWhOcIIRXQKuSvaSpoPWE+jIwGahJmMkmk+gdszoXjrY4IKa9J0pNAA6vgirLXDSzUTRZu4jqYGg/q2vTUZFNu6B/z7NcAN4eWi4cLDJ7qyyOiO1hMJp4a8NxAP5yyRAenDMYHw/HLoAQXw/+u3ACI/sEUVnfwu+WbyezQGa8JBLJOUjtKcj8SqyrTrhnMS6Lroceeoj333+ftLQ07rnnHu655x7S09N59913eeihh05HjG7hmWeeYcIE53NwJBKJBGwlhmp2S80KaRUtXtqOM/l9AvoAkFWZRXZVNgoKoyI77zMaEiLMNArrCilvLAfgl5O/YDAZ6B/Un/7B/ducE+sXS7h3OAaTgf2l+51eVxVd1wy8hi/nf8mSiUsA2FzQtlKhUwbNgZC+rp/XFTx8IGmKWNfo0cx+xrprmCq6hl8DHn5QdtQ2WHnbG2KpWLJRuTscr2tsgdUPw/4v2r21OquroKqBxhYjTQYjO7KF6JrsJtEFtt6w7zspMfx+fxEny+sJ9tGzYGx8u8cFeuv54NbxjEsKoabJwDOrnLtfSiQSyVlNxkdgaoGYURBzmudSngG65bt47bXXsnnzZsrLyykvL2fz5s1ce+217o7NbWRlZXHo0CHmznUyQ0YikUgsqGYaaqbL3rmws6xbvH88CgpNxiYABgYPJNCz8xlTfh5+1ixZZlkmWwq28OKOFwFRWugMRVFIjUgFnJcY1rXUWbNtU+OmolE0XJp0KVpFS1FdEYW1HWdczjipvxXLyffiGzOYfuG+eOk1jEoIFts9/WH4b8T6rnehcK+wmle0MGGR2J7Xymn24New7V/w5R1QcQJnhPl54Oepw2yGvIp6dp+spLHFRJifJwMjO85susKFgyLw1GnIKavnSLHzMkiz2cwb648B8IdJiW0yXK3x89Tx8rUp6LUKm4+WsSO73G3xSiQSSa9jMkHau2J9zC29G4ub6HWz+w0bNjBv3jxiYmJQFIWVK1e2OWbZsmUkJibi5eXF+PHj2bFjh5Mrtc8DDzzAc889566QJRLJOUpr23ir6NJ3/gHcS+dFtK+tdK4jq/jWqH1dr2e8zp9+/hM1LTWkhqdyw5Ab2j2nIzONbQXbMJgMxPvHWwWdj96HQSGD2j2nVxl2Ndx/BC58BIDP7pjET/dNI8zPzpxDLS05+A2sfVasJ8+HoVeK9bydttJDgCOiJw5jE6x5wultFUUhMUyYaWSX1lv7uS7oH+rW0lZfTx0DI0VPYH5lvdNjNh0t5UBBNd56LX+YmNil68YF+/CbMSIj9urPR9wSq0QikfwqOP4LVOSAZ6D4G3EO4LLoMhqNLF26lHHjxhEVFUVISIjDy1Xq6upISUlh2bJlTvd/8sknLF68mMcee4z09HRSUlKYPXs2JSUl1mNSU1MZNmxYm1dBQQFfffUVAwcOZODAgS7HJpFIzi+s5YXNjuWFXRFdYCsxhK71c6moDoZ7S/diNBu5vN/lvD377Q77yKxmGqcyrH1nKhvyRWnhtLhpDuJhVIQod+xMdBXUFvDziZ9pVocinwn8I4WbIaJvKT7Ex3F/dIooMTG1wJHvxbYJi4SNvdoTVi76oTAZhRuiyv4VkLfL6W0T7WZ1bbKKLveVFqoE+egBqKxvcbpfzXItGBtPsG/XZ9PdeWF/9FqFLcfK2H68rPMTJBKJ5GxglyXLlXq9KEM/B3BZdD3xxBO8/PLLLFiwgKqqKhYvXsxVV12FRqPh8ccfdzmAuXPn8vTTT3PllVc63f/yyy+zcOFCbr75ZpKTk3njjTfw8fHhnXfesR6TkZHB/v3727xiYmLYtm0bH3/8MYmJiTzwwAMsX76cJ598st14mpqaqK6udnhJJJLzg9Y9XTUtwma9MxMNFdXBEFyzux8RLuZfKSjcO+penr7g6U6HQg8KGYS3zpua5hqOVx63bjeZTdZ+rilxUxzOUUsSOxNd9669l/vW3cf8lfNZc2JNl6zOzwj2jdQxI4Wzos4DYsRzWfu68nZCQwV4Bdoshn/4i2MmzEJiqC8aTJQd28XeXFGidzpEV6B3+6Jrb14lm4+WodMo3DYlyaXrxgZ5c60125XV80AlEomkt6nKg8OWL9dGn/0GGioui66PPvqI5cuXc//996PT6bj++uv597//zZIlS9i2bZtbg2tubiYtLY2ZM23DPzUaDTNnzmTr1q1dusZzzz1Hbm4uOTk5LF26lIULF7JkyZIOjw8MDLS+4uPbb2aWSCTnFmpGSxVdasarq5kutZSvf1B/gr2Cu3zfEWEjeHTCo/z74n9z6/Bbu1TaptfoGR4mXP7SS2zOfQfLD1LaUIq3zrtNtk3NjmVVZrU7tyuvJo+D5QfFem0e9667l1t/vJUT1c77os4ow64GT4tl8PhF1syY1dY+d7tYqqWF/WfBzMdB7yP2qS5YdiSG+vCa/p88dGIhlylbSArzJTbI2+2hW0VXQ1vR9e7mHAAuT4khLtj1b3T/ZMl2bT1exjaZ7ZJIJGc7u94VrrSJUyBicOfHnyW4LLqKiooYPlz8offz86OqqgqAyy67jO+++86twZWWlmI0GomMjHTYHhkZSVFRkVvvpfLwww9TVVXF0qVLGTRoEP37t3UOk0gk5ybqAGRnRhpdYU7SHMZEjuH2lNtduq+iKFw76FrGRY9z6TxnZhpqlmti9MQ22bIInwhi/WIxmU3sPbXX6TXX560HxIDqP474I55aT3YW7eQvm/7iUmynBQ9fMYz5okeFo6FK/HixVM00VNE1cA4ExMCke8T7n5aAocnhkqOrfmCeVnxhOF5zkAv6hzre09AMOZvFsgeo5YXVTkTX4SIhgC8dEd1mX1eIDfK2uh3K3i6JRHJWY2gS40EAxi3s1VDcjcuiKy4ujsJC4XzVr18/fvxR1M3v3LkTT0/Pjk7tdW666SaWLu14Ro2npycBAQHcf//9HDp0iLS0tDMUnUQi6W1aZ7pcMdIACPMO49057zqdrXU6UDNXO4t3Utog+pE25glL9alxU52e01lf1/pcIbpmJczi7pF38/GlHwNwoPRAuzPBzigDZsHUB0BjN7g43iJWSzKhOBNKDoCigf4zxPYL7gG/KKg8AZ/dBM0WM4vKXBK2P269zEBNflur+G3L4L1LhBNiDwjyFgK4sr6teFO3hbjQy9WaP03vj6LAtuPllFQ3dusaNY0t7Mgu59NduZwsc274IZFIJKeVAyuhvhQCYmHQpb0djVtxWXRdeeWVrFmzBoC7776bRx99lAEDBnDjjTdyyy3utXQMCwtDq9VSXFzssL24uJioqCi33qs1y5YtIzk5mbFjx57W+0gkkl8PbdwLXTTSONOkhKfgq/elqK6IuSvm8sy2Z6xzu1r3c6l01NdV21zLzmKRLZoWNw2AfkH9CPMOw2g2crj88Ol4jJ7jHwWBfcBsgnUWZ8P4CeBjMXfy8IUrloHOSwxV/uBKqC+HlYvQNNeQhxhePFDJY2JSq0zXCUspe+GeHoUY6NN+eWGFpc+rJ6IrJsibARHi93RPXpVL5763OZvpL61l+OM/cu2bW3nw871c/Op63t+Sg8n0K+nnk0gk5wc73hLLMTeDtuPRGWcbLouu559/nr/8RZSZLFiwgI0bN7Jo0SI+//xznn/+ebcG5+HhwejRo60iD8BkMrFmzRomTpzo1nu15s477yQzM5OdO3d2frBEIjknaD2nS+176mp54ZnG38Of12e+zoiwETQaG/n48MeYMTMkZAgRPhFOz1EzXftK99FichQAWwu3YjAZSAhIIDEwERClj8NChwFwoOxAh/G0GFs4Xnm8d4w34i1fkB38RiwHtppx1n8m/P5LYa6Ruw3+MUoMWtb78lzQkxjMGgKUegKNpY7nFe0Ty4qcHoWn9nRVtRJdjS1GGlqMAAT5dF90AaTEBQGwJ7eyy+f8lFnM499kkmPJbEUHejE4yp/GFhOPfX2AG9/ZQWHVryDDKZFIzn3y0yB/F2g9YNRNvR2N23FJdLW0tHDLLbeQnZ1t3TZhwgQWL17MvHnzuhVAbW0tGRkZZGSInoTs7GwyMjI4efIkAIsXL2b58uW8//77HDx4kEWLFlFXV8fNN59eNxOZ6ZJIzj+s5YUWAw21zPDXmukCUWL44SUfWsUXwJUDnLvBAvQN6ou/hz8NhgaOlDv2/6zLXQfYslwqyWHJgCgx7Ii/pf2N+V/N56ltT7WxsT/txLXqh2stugASJsHNq8E/WrgbAsx5Fs/oZHLMluqJkoO24+vKoKZArDsTXc11sOkVqO582HSQKrpauReqboZajUKAV8++1U3tYxFdeV0TXUVVjTz4ucjg3TChD2l/ncnWh2ew6p4pPHH5ULz0GjYdLWXOqxs5WuJ8qLNEIpG4jR3LxXLoleAX3ruxnAZcEl16vZ4VK1a4NYBdu3YxcuRIRo4UvQmLFy9m5MiRVofBBQsWsHTpUpYsWUJqaioZGRmsXr26jbmGu5GZLonk/KO1kYarlvG9haIoTI6dzIeXfMiGBRu4btB17R6rUTTWXjB710OjyWjtB5seP93hHHWO2P6y/e1et8nYxFdHhTvgZ0c+45FNj2AwGbr1PN0i3k50BfWB8HYcryKT4dYfod9FwgFx1B+4Z8YADKFicLSD6CreZ1tvKIfGVmV7O9+Gnx+HVQ90Gp6axWpdXlheJ/q5grz1PR7IbJ/p6qws0Ggys/jTDCrqWxgaE8CjlyUTahlGrdEo/GFSIqvumcLQmACqGlp4+Iu9stRQIpGcPupKxUxFgHF/7N1YThMulxdeccUVrFy50m0BTJ8+HbPZ3Ob13nvvWY+56667OHHiBE1NTWzfvp3x48e77f4SiUSi0lPL+N5GURSCvYI7/fCuii77vq59pfuoaKrAX+9v7ftSUUVXTlWOtc+tNety11HbUou/hz9aRcu3x7/lgfUPnLkBy1HDQWexeh84x2Yn74ygPqLUcO7zoCgkhvkyeIRFtJ2yE11FrURmRSvb/GJL5i/rJ2hybsGvYl9eaF9+qZpouDIQuT0GRfnjqdNQ3Wggu6yuw2Pf3HCMLcfK8NZr+fv1I/HUadsc0zfcj7duHIOPh5adORX8b+fJHscokUgkTkl/H4zNYgZjbNfnXJ5NuCy6BgwYwJNPPsk111zDc889x9///neH17mCLC+USM4/2hhpuOheeLZgL7pUAaBaxU+OnYxeo3c4PtQ7lGjfaMyYrTO8WvPtsW8BWDBoAa9MfwW9Rs+ak2vOnNW8Vi+yVygw9CrXz1czYyWHbNuK9jke07rEsNRSnmlsgqwfO7y8ahlvNJmpbbJlAFUTjWAfvdPzXEGv1TA8NhDouK8rs6Cal38UsT9x+VD6hbf/+x0b5M3/my2ygM+vOkRRVfecESUSiaRdDM220sJxt3f8pdlZjMui6+233yYoKIi0tDTeeustXnnlFevr1VdfPR0x9gqyvFAiOf+wz3SZzWarkYa/h39vhuV2hoYORafRUdpQyv3r7yetOM3WzxU/zek5w8IsZhpO+rrKG8vZlL8JgHl953Fhnwv554x/AvBDzg/WzOFp54p/waItkNANo6WIIWJ56jComahiS6bLSwgZB9FlNkPZUdt7J4OX7fHSa/HUiT+5lXZ9XRWWTFdPTTRUUuI7N9P4ak8+BpOZmUMi+M2YuE6veePERFLjg6hpMvDY1+2XmEokEkm3OPAl1BSK0R7Dru7taE4bLouu7Ozsdl/Hjx8/HTH2CjLTJZGcf6iZLpPZRIOhwSoW1O3nCl46L64ZIIYL/3TiJ25afRNHK4+iVbRMjp3s9JzkUIuZhhMHwx9yfsBgNpAcmkzfoL4ATIqZRIiXsGzPqc7pNCa3GG94B4mere4Q0g80Omiugao8MaDzlCXrNXCuWFbYTKSoLYamatv7rJ9s87/aQc122TsYVlh6utyR6QKb6MrowDY+LUeYiMweGtWlPjKtRuH5q4ej0yj8cKCY1fs7Nw6RSCSSLmE2w1bxJR3jFoLOPV9A/RpxWXSdL8hMl0Ry/uGt80ajiH8Wq5qqaDSKUqpzLdMF8MiER1hx+QquHnA1nlphoDA2aiyBnoFOj1czXeocMHvU0sLL+l7msD0xIBEQvWAdsebkGkZ9MIoPMj9w5RHci84DQgeI9VOHRMbLZBBZrkSLELXPdKmlhcFJokespR6O/tzhLZzZxlvLC93Q0wWQajHTOFhQTZPB2GZ/k8HI3nwhyMYkhnT5uoOjAlg0vR8AL/90pJOjJRKJpIvkbIKivaInd4x75/3+2nDZn3bx4sVOtyuKgpeXF/3792f+/PmEhHT9H3OJRCL5NaAoCr56X2qaayiutw1lP9cyXSoDgwfy+KTHuXfUvWwu2MyYyDHtHjskRJTf5dXmUdVUZRVnOVU57C3di1bRMjdprsM5SYFJpJekk12V3eZ6Ki3GFl7a+RJGs5FX015lSuwU64ywM07EYGGkUXIQakvEtsjhEJIk1h1EV5ZYhg2EsAHim9qDX0Py5WJ7dQGsfUYMaU79HWg0BHlbHAztygutRhpuKi+MD/EmxNeD8rpmDhbWkGrJfKnsz6+m2WAi1NeDxFAfl65925S+/GvdMY4U15JXUU9csGvnSyQSSRu2LhPL1N/aBtqfo7ic6dq9ezdvv/02b731FuvXr2f9+vUsX76ct99+mzVr1rB48WL69+9PZmbm6YhXIpFITitqX1dRXREgsl86Tc/mJ/3aCfIK4tK+lxLp2/4ojkDPQPr49wEc+7q+PS6yXBNjJhLmHeZwjjXT1UF54YqsFeTX5gPQbGrmqW1P9c5wZYBwta/rkK2fK2o4BCeK9cqTYLJkj6yiawAkzxfrh1eLssSGSvjgKtj9IXx9F7xzMRTuJdBSQljZYHN0rKhvZrhynMl5y8HYc4t9RVFIiWvfTCPtRDkAoxI6d7lsTaC3nlGWWWDrDp/qYaQSieS8p/QoHPlerE/4U+/GcgZwWXTNnz+fmTNnUlBQQFpaGmlpaeTl5TFr1iyuv/568vPzmTp1Kvfdd9/piPeMIXu6JJLzEzWrpYquc825sCcMDRPW8Wpfl9lstoqu1qWFIDJdQLuZrgZDA2/ufROAm4behJfWix1FO/jm+Dduj71LRKgOhgdtzoVRw8QwZa2HKDesFgLRWl4YNhBix4B/jOgHO7IaPrlBZMx8wsDDD/J2wlvTuKHqTRRMDuWF5XXNvKb/J8OyXodD7nnujsw00k6Ifq4xCcHduvb0QREArDtc0s3oILe8nrc3ZZNb3nEPnEQiOcfZ/rpYDpwLYf17N5YzgMui66WXXuKpp54iICDAui0wMJDHH3+cF198ER8fH5YsWUJaWppbAz3TyJ4uieT8RBVZannhuVpa2B3UeV0Hyg5gMpt4etvT5Nfm46Pz4aI+F7U5Xi0TPFl90qlRxseHPqa0oZRYv1juGXkPd6TcAcBLO1+iorHi9D1Ie4TbORhaRddw0GhF3xbYSgzL7DJdGg0MmSfef3kH5GwED38xC+yuncLC3mxiWtmnzNHspMquvDC89hB9NUWWax5rG1NeGnzzZ6gv7/Jj2Mw0HEWX2Wy2iq7R3RZd4QBsOVbmtGesI1qMJv617iizXlnPU99mMuNv63nimwOU1TZ1KxaJRHIWU5kLGf8V6xPv7N1YzhAui66qqipKStp+w3Xq1Cmqq4WTU1BQEM3NZ2ggpkQikbgRXw/HTNe5aKLRXVQzjX2l+3h448N8euRTFBQeHv8w3upgYjti/WLRaXQ0GhutP0+VmuYa3t7/NgCLUhah1+q5ceiNDAgeQGVTJX/b9bfT/0CtCekrMlotddBYKdwM1fldaolhRY5wKazMFe/DBoqlWmLYUi/OW/AfiB4BATHwm3dh0t0AXKtd59DTNalxve3+reeAAWx4EdLeg4yPuvwYqpnG8VN1DgLvRFk9pbXNeGg1DIt1bpjSGcnRAUT4e1LfbGRndteFcdqJci79+0ZeXH2YxhYTMYFeNBtNvLs5h6kvruWtDU4Ep0QiOTcxGeHL28W/l/ETbGZF5zjdKi+85ZZb+PLLL8nLyyMvL48vv/ySW2+9lSuuuAKAHTt2MHDgQLcHK5FIJKeb1pkuWV5oY0jIEDSKhpL6ElZlr0Kn6Hhh6gtc0f8Kp8frNDprH1jrEsMPMj+gqqmKpMAka2miXqPnsYmPoaDw1bGvKKnvuIStxdTCN8e+Ibcm1w1PB2h1NgdDEIJKJ5wdHURX+THADF5B4BMqtveZAIHxYn3+MsugZjtG3wzAVM1eqBEligaDkYvNW2zHVJ5oG5M6C6z1oOYOCPb1IMFikrE335btUrNcw2ID8NJru3w9exRFYdpAke1a28USw+Onarn+re0cKa4lxNeDl69NYfNDF/HhreMZHhtIXbORZ1cd4uMdJ7sVk0QiOcvY/Cqc2CzKr698/Zwdhtwal0XXm2++yYwZM7juuutISEggISGB6667jhkzZvDGG28AMHjwYP7973+7PdgziezpkkjOT6yiq84iujyk6FLx0fvQN1DM4fLUevLaRa+1cSxsjdrXZW+m0WRs4j+Z/wHgrtS70GpsAiAlPMVq6NGR6Go0NHLf2vv4y6a/8MD6B7r1PE5R+7pAlBaq2Isue+dC9cOCRgs3fQcLf4GU69peN7QfpaFj0CpmRpavBqD2+FbilFLbMRWtRJfJaNtW5NpQ4hRLtmtHtq0scZfaz+WCVbwzLhzsWl/XSz8cptloYnxSCL/cP42rRsWhKAqTB4Tx1Z0XcM8MIXSXfH2AfR3MF5NIJOcA+emw9lmxfslLosLgPMFl0eXn58fy5cspKytj9+7d7N69m7KyMt566y18fUVZTmpqKqmpqW4P9kwie7okkvMTtYfrVINwZ5OZLkeuG3Qd/QL78frM15kaN7XT41UHQ/tMV0ZJBnUtdYR7hzMzYWabc4I8hWBor6+rurma23+6nfV5ojQvsyyTg2UHXX0U56h9XQCRw2zr7Ykue4ITqqxt+QAAIABJREFUIHZ0u5cuG3AtAFPrfhADQfetAGAHoleOqjxHB8OqPDBZygNLDwtnxC5y4WCRjXpnUzYFlQ2Azbmwu/1cKhf0D0OrUTh2qq5TM4y0ExV8v78IjQJPXTGMoFbW+BqNwr0zBjBzSCTNBhN3fJhmHRgtkUjOMZrrYMVtwpRo6JWQcn1vR3RG6fZwZD8/P0aMGMGIESPw85MfSiQSybmBKrrMmB3eSwQLBi9g5RUrGRvVtSoAa6bLbkDytsJtAEyInmAdRm2POgOssqmt+15pQym3rL6F9JJ0/PR+DA8T2agvj37p0nO0S7uZLrtZXVbnQtfctpoHzaPW7EWMqRByNuJzVLgVfuk5X/SSmY02d0SA8uO2dZPBdt8uMD8lljEJwdQ1G1ny1QGqGlo4UlwLwKg+PRNdgd56Rluu0VG2y2w289wqIYavHRPPwEjn/ZEajcLfrk0hIdSH/MoG/vxJBkZTL40NkEgkp48fHhHl2QGxcNkr501ZoUq3RZdEIpGci7QWWdJIo2c4s43fVmARXTETnJ6jZrqqmtqWmv110185XHGYUK9Q3p3zLnel3gXAd8e/o8noBhc8+0yXg+hKEMv6MihIF+utM12dEBgQxDfGieLNd/fj0XCKSrMvR/zH2/rB7Pu6KlpZ7bcuMSzNgm/uherCNvfSaBSevWo4eq3CzweLreInMdSHcH9Pl+J2xnRLJq2jeV0/Zhaz60QFXnoN983q+GcV6K3njRtG46XXsOHIKd7bktPjGCUSya+IrJ8h7V2xfuUb4N2zL3/ORqTokkgkEjtalxPK8sKeodrGlzSUUNdSR1VTFZnlmQCMjxrv9BxVdDnLdKkzwl658BUGhwxmfPR4onyjqG6uZu3JtT0POLQfjF0Ik+8DX7thz57+Yu4W2DJQrooubz2fGaeJN5as1ffGcfj7+thEnX1fl32mC2wDm1XWPCk+xKx50un9Bkb6c8e0fgB8vFOYjYzqYWmhyvSBoq9ry7EyGlvaWscbjCZeWH0IgNsm9yUywKvTaw6JDuChOSLT+HlanlvilEgkvwIaKsSgeIDxiyCp89L0cxEpuiQSicQO1TJeRRpp9IwAjwBCvYTDX051DruKdmEym0gKTLIaZrSmPdFlMBms21RXRK1Gy/x+wq79i6wveh6wosClS2Hm4233qX1dIGzh7d93AX8vHbsZwFFTjHXbt6YJhPh4QJBFdNlnusotmS4142bvYGgyQvYGsX7gS2h0bkBx54X9SQqz/U6PSeiZiYbKkGh/IgM8aWgxsiunbe/dZ2l5HD9VR4ivB7dP63qj/PzUWLQahYOF1Zwsk8OTJZJzglUPQk2hcIed+VhvR9NrSNHVDtK9UCI5P5GZLvejZruyq7LZWrgVEP1c7dGe6FLfKyjWYwCrZf22wm0U1BY4vWZJfQkfH/qYlUdXsi53HbtLdtNgaHDtQexFVnASaPUuna7RKAR6e/CpJdtVpwtmmylZmEs4zXRZRNcQywyw4v3CgAOgcI+YJQZgaIB9nzm9p5deyzNX2gxBxiS6J9OlKAqpliHMx07Vttm/5qDo9bp1chL+Xl3/OQX7ejDO4q74w4GiTo6WSCS/ejK/gn2fgqIRZYX6tjMdzxek6GoH6V4okZyftBFdMtPVY+zNNLYXbgc6Fl3tGWmoboaBnoEONvNx/nGMjxqPGTNfHf3K6TVf2PECz2x/hkc3P8rdv9zNjd/fyE2rb3LtQexFl4ulhSqB3no+Ms6ktP9vWBF9P0a0BPvo22a6zGZbT9egueIDS30Z1FiEyPF1Yqm1uAGm/6fde07qF8bzVw3nkUuGtGtm0R2iA8WHp6Lqxjb7iqqFoB3UjfvNGRYFSNElkZz1NFTCt/eJ9cmLIW5M78bTy0jRJZFIJHa0NtKQma6eo9rGby3cSk51DhpF06H7YXtGGqroCvZqm625YoDIdq08uhKT2dRmv9oLNiJsBMNCReYnsyyT8sbyNse2i4Pocs25UCXIW08d3mSMeoZNemGqEeTrJNNVWwwt9UJshQ20DW1W+7pU0TV5sRBehXugIKPd+143rg8Lp7p3Hk5UoOjTKqpyIrqqmhyOcYWLh4qy07STFZTUtL12ezQZjJwsq2dHdjlf7yngi/Q8jp2qxWyWTogSSa+Q9ZP4siikL0z7v96OptfR9XYAEolE8mtCZrrcj5rp2ntqLwDDwoZ16AqpiqrWma7yJiGQgj3biq6ZfWbyrP5ZCuoKSC9OZ0yU7RvV+pZ68muFFfs/ZvyDEK8Q5n05j5zqHA6UHmBK3JSuPYg7Ml2WOVWVDS1U1It5VKKny3Lt2iJoabCZaATGg84DooaJWV1F+yBxMpwUDpAMuxrKsmD/CpHtijlzMzKjLYKqsMqxTLPZYKK0tsnhGNeu601KXCB78qr4KbOY341P6PScI8U1XPWvLdQ2GdrsC/H1YExCMLdOTmJ831CX45FIJN3k6M9iOeRy8e/YeY7MdEkkEokdbYw0ZKarxyQFJDm876i0EOzKCxudlxeGeLU1g/DSeVkt6NWslkp2dbb1PPXcoWFDnR7bIW4QXUHeor+pqqGFinox+DjYRw8+IaAK/MpcWz9XiOVnpw5qLt4vBJexCfxjIGwAjLpR7Nv3GTSfOfOJKIsjYXG1o1V/saXc0EOrIcS3ex+0Lh6qlhgWd+n497bkUNtkwEOnISHUh3FJIYxNDMZDp6G8rpkfM4u56d2dHHfSfyaRSE4DJhMcWyPW+8/s3Vh+JUjRJZFIJHb46qTocjcxfjHoNTYzhc5El1pe2GhspNFgKy/rqLwQYGCwEEKHyw87bD9WeQyAvoG28rqhod0QXQEx4BMKeh8IH9T18+wIVEVXfTOVlkxXkI+HcE207+tSM10hlpitouuArbSw73RxXuJUIQibqiFzJZw6Alv+AZ/fArk7uhVnV4iyy3TZl/CpPV5RgV4o3Rx+qvZ1bT1WSlVDS4fHNrYY+WaPMFB576axrP9/F/Lp7RP57I5J7Hv8YlYsmsS4pBAaWoz8+eMMmg1ty08lEombKdoLdafEl0nxzseDnG+cF6IrMTGRESNGkJqayoUXXtjb4Ugkkl8xWo0Wb50wCNAqtnVJ99FqtCQECEHhrfMmJTylw+P99H7oFFH9bl9iqPZftSe6BoeIGU+HKg45bFdFV7+gftZtw8KEiDlQ2rHo+iHnB8Z9NE4YdGi0cMuPcNvP4BXY4XntEeQjRFdFvV2my9ciSK19XTk20RVsyXRFWURXaRYc+UGs950ulhoNjPy9WP/6blg2Fn78qyg5fH8eHPy2W7F2hjp7q7HF5CCMCqtsoqu79Av3o3+EHy1GM2sPlXR47A8HiqhpNBAX7M2EVuWDnjotoxOCee26VAK99ezLr+LVn490Oy6JRNJF1NLCpKmytNDCeSG6ALZs2UJGRgZr17pheKZEIjmnUbNbvnrfbn9TL3FE7esaFTkKD23Hf4AVRbGWGNqbaaiiy1l5IcCgYJF9yq7MptnYbN1+vFIIGHvRNSh4EBpFw6mGU5TUO/9QbzKb+Mfuf9BgaOCZ7c+QW5MrDDQih3YYf0eoma68inqMJpEdCrb0eTlkulTnQjXT5R8N3iFgNsKpg2Jb32m2C6f+DrSeYDIIY42+F0LiFDA0wqe/h13vtB/Uplfgs5ugpeumFSDs6NXywUI7M40iS49Xd/q57JltMdTozMXws11ikPLVo+LQaJz//xod6M3zV4l5Z6+vP8a242U9ik0ikXTCUbW0cEbvxvEr4rwRXRKJRNJVVAfDjsweJK4xNW4qAFf0u6JLxzub1WUtL3RipAEQ5RuFv4c/BrOB41XHrduPVh4FoF+gTXT56H2sImx/6X6n19uYt5ET1cJNsMHQwKObH3XqjOgKqujKsQz+9dZr8dJb7O/tHQxblxcqii3bBRA+BPyjbO8DouGW1XD9x/BgNty4En6/UmTAzCZh27z+xbYB1Z6CNU+JAcuHv3P5edRsl71tvDsyXQBzhkYDsO7wKRpbjE6PyauoZ/OxUgCuGR3X4fXmDo/m2jFxmM2w+JOMTssWJRJJN2msglwxHoR+UnSp9Lro2rBhA/PmzSMmJgZFUVi5cmWbY5YtW0ZiYiJeXl6MHz+eHTtcq1FXFIVp06YxduxYPvroI3eFLpFIzlHsM10S9zC/33y2/XYbc5LmdOl4NdNV0VRh3WY10vB2nulSFMVWYlguSgwbDA1W50L7TBd03tf1QeYHAMxNnIu3zpu04jT+e/C/XYq/PYIsWa3cciG6gn3sBgerRh2FGeJDi/02gMjhtvW+09tePHaUmOnlaelD1Org8n/A1AfF+7XPCGt5ew58IbJnAJlfu/o41mxWkUOmS6xHB/RMdA2LDSDQW09Di5Gcsjqnx6xIy8dshol9Q4kP8en0mo/NG0pCqA8FVY18mZ7Xo/gkEkk7ZG8Q/66E9reZAUl6X3TV1dWRkpLCsmXLnO7/5JNPWLx4MY899hjp6emkpKQwe/ZsSkps5SCpqakMGzaszaugQDTWbtq0ibS0NL7++mueffZZ9u7d2248TU1NVFdXO7wkEsn5hepgKE003IeiKC6JWOusrkZbeaEqwNrLdIGtxFA108ipysGMmSDPoDZlieq8Lmd9XYfLD7O9aDtaRcviMYu5f/T9ALyW/ho5VTldfo7WqD1dBrW00N7dz1peeFIs/aPBw05I2Ge6+k7v2g0VBS56BJItGcadbzvu3/uJbT3rJ2FX7wI2Mw1nma6e9UMqikKEvycAZbXNbfabTGY+T88F4NqxHWe5VHw9dSwYGw/AlmOyxFAiOS2o/VzStdCBXhddc+fO5emnn+bKK690uv/ll19m4cKF3HzzzSQnJ/PGG2/g4+PDO+/Y6tMzMjLYv39/m1dMTAwAsbGxAERHR3PJJZeQnp7ebjzPPfccgYGB1ld8fLwbn1YikZwNqGJLlhf2Hq1ndZnMJut6ez1dYHMwPFIhzBKspYVB/dr059nbxrceoKtmuWYlzCLKN4rfDPoN46PH02hsZMmWJd0euKtaxqtY+7kAgvo4Hhzc6hviKEumS6ODhEmu3XjcH8Vy32e2LFrZMchPA0ULvuHQUgfHfnHpsmo2q9hZpquH5YUAoX7i56PO/bJne3Y5ueUN+HvqrKWIXWFSvzAAth0vs/bVSSQSN2E22/VzSdFlT6+Lro5obm4mLS2NmTNt/9E0Gg0zZ85k69atXbpGXV0dNTU1ANTW1vLLL78wdGj7TdAPP/wwVVVV1ldubm7PHkIikZx1qBkZWV7Ye1hndVmEVlVTlbWfKsgrqN3zBoWITNeh8kOYzWZrb5d9P5fKwOCB6DQ6KpsqrSWIAKUNpazKXgXA75OFK6BG0fDkpCfRKBp2l+ymtKG0w/jNZjM5VTkOhh5g6+lSCbIvL/T0A58w2/uQvg7HEjkMLnwE5r0GXgEd3r8NCZNEH1hLPez5WGzb+6lY9rsQhl0j1g9+43je0Z/h58fB6Lz/KVLNdFl6ugxGEyU17hNdYX4i01XqJNP1WZr4+3xZSjTeHtouX3NYTAB+njqqGw1kFshqFomkR1TmwjtzbSMqTh2Gqlxh7JNwQW9H96viVy26SktL+f/snXd4W+XZ/z9HkiUvyTO2Y8eJs/deBBJIgBQChLJXC2UUWspoG2gLbYGWt6W0BX4vbVNW2bOU/bJpIAMSsifZw4733kvW+P3xnOeco2VLjkPW+VyXL8vS0RmSAs9X3/v+3l6vl+zs7ID7s7OzqajoPs1IUllZyezZs5k4cSInnXQS11xzDdOnT4+4vcPhwOVy8eKLL3LSSSdxxhlmA6CJyYmG6XQdeYKDNGQ/l9PuDJj5FczQ1KHYFBtN7iYq2yo1p2tI6pCQbe1Wu+aMGfu6/r3r33T5upjYbyIT+k3Q7s9NziXFHigGw1HWUsbN/72Zhe8s5IHVDwQ85urO6QI9TAMgvSDwMUWB034Jk78f8dgRURSYfoO4vfZfYnCpLC2ccDmMOV/c3vUheFSB01gC/75GpBtKgRaE3tMlyhKrWzrx+cFmUchIOPQlhi66Qp2uVWp54PkT88DrgRUPh/ashcFWu5v/SfsQB25W7utePH/rtDdAaeRqHBOTowqPWySfHlwpRlQ8PR+eP088VnBKYHm0ydEtuvqCIUOGsHnzZjZv3sy2bdv46U9/GtXzbrnlFrZv387atWsP8xmamJgcbcgwBvnb5NsnWHT1FBcvcVgdFKQUAKIvS8bFD0sdFnb74L6umvYa/r1TiJFrxlwTsn24KHuJ1+fl5R0vc8G7F/BV2VcAfHTgowC3Kz7OSkKc7soE9HSB3tcFoU7XoTLhcohLgprd8NX/ilj6uEQYeY4YXprUT5QeFi4X2398lyg5BBG4EYbgIA3Rz+XngYSXsP4xC545G75+HJrKe3XKmbK8sDlQdPl8fqrU+wZnJsHuj2DJ/fDihdDajZDqaIQXL+TChuc41/J1TH1dnR4vn35TwXuby7SfHeV97JT93+3w1LzuI/5BiLOXLoFP7+nb4/cFnk793HpZhmtyjLDk91C6TswtnHilGFfRWi0eM1MLQziqRVdmZiZWq5XKysqA+ysrK8nJyYnwrL5h8eLFjBkzpltXzMTE5PjkwuEX8sVlX3DJiEuO9KmcsGhBGqq4iSZEQyJLDDdXb6akRSTUBScXSox9Xe2edm5bchv1nfUMSRnC6QNPD9ne5RBlfY3uUNH1u1W/48E1D9LuaWdK1hQyEzJp87SxpiIwcddYYhiQXgiBTldwT9ehEu+CiZeL25//j/g96jxR1mixitsgSgx3fyp+K+oyYf9SaKsL2aWMjG/q8NDa6aGisYOfWt/iMu8HgB8OroKPfwWPjIbHZ8M7P4FV/xTpZsb9+f1wYAW8+UN4ZCzsFPH10umqbQ0sL6xtdeP1+VEUVZjVqXPN2mrho19Gfg0+/S00i5CtAksFawvr6PJGNwbgoU92cdOL67n91Y3azzl/W8FfP9mJJ8p99Ei5GvT1yW9Ez104/H7xOu79DL7+p3AtY+Htm4UYbul+6DTlm+Ff8/Vy1GgpWSfObeXfYP1z3W+75XX45yxRlhYLtfvg8Tmw5qnut/P54ONfw+KZYjxCLOz+FJ46Q3wuu6OjEZ4/Xwwi94UfbRCRZX+BJ+dBzd7ut6veDf88GT67N7b9+3zivJ5ZEPbf7yGx80NY9Q9x+7v/hAsfh59/A3N/Ldz4KaFfWp3oHNWiy263M3XqVJYsWaLd5/P5WLJkCbNmzTqsxzadLhOTE5vMhMyeNzI5bMi+Lc3pahcLBhmw0R2j0oRD+WnRp/j8PlIcKWTEZ4TdVsbGb6/dzt0r7mZb7TZSHan8/fS/Y7PYQraX5YVNnaEOxyeFnwBw57Q7efbsZzk9X4i2Lw5+EXhtiUbR1Z3TdRiilqepJYZy3tiEy/THZInhjvfhwzvF7Vm3iAAPnwd2hEbKO+PjSHaI16miqYOUb17k53FvigfP/D2c9SfhouGHiq2w6WX45G6xEPzLYCGwXr4M/j5FlCVt/Q80lcD654HI5YWybywjyYHNaoEmvSePbW+Kawhm3+ew4QXtzyG2OtrcXraURC4VldS1unnpa5EqOW1QGicPzWDKwFT8flj8xT6uePJryhpiS34Mwe+HJiEI6WqDt24SZZPBfPWoPlPN5xFCM1q6OmDzK0IMv3iRcMzCUb1buIYla3p23YKR1wDCLa0IPweP7e/B2z+Cqu3iPYuFHf8HFVvE53Tds+G38fuFyP56MVTvFF8cxMLGF4SL88rlQkiGw90Gr1wBB5aJLxLqC2M7xtp/QdkGePEC0RsVjoaD4vGqb2DDi7Htv6FInNfBlfDSRdDRR85sw0F452Zx+6SfwGj1C5vkLJj7K/ju4tj7Tk8AjrjoamlpYdOmTWzatAmAAwcOsGnTJg4eFP9xW7RoEU899RTPP/88O3bs4Oabb6a1tZXrrrvusJ6X6XSZmJiYHDm0II0OVXR1RldeCDAiXfRpycHGQ1NCkwslQ1OH4rA6aOlqYcnBJcRZ4vjb6X9joGtg2O0jlRd2eDpo94hF90XDL8KiWJg3cB4AS4uXBqQdGp2u1MQ41las5c9r/iz2KZ2uhDTx09fkjIOB6peWiZkwZJ7+WMEciE+FthqxWHPlwWl3wdiLxOPBC2OvB6p3MTO5iuFKCb4NL3HyTtHDtrz/9TD7ZzDrJ3DDp7BoB1z+Epz2Kxh5rp7U2FQCez4Rw6DtyTBigbi/XKwJMiKUF8rSQhkpT6M6cytF3e/7Pw/8Zr+zGd67XdxWHcSRCeKztXJvz6LluZWFtHd5GZfn4j8/nsUrN57EWz85hX9cNRmnw8a6onrO+dsKVu8/hBj61hrwqtfpSBEL/i8fCdzmwApR0gWA+plujqF0s9kgiCq3wiuXgTtoBppc5EsxF8v+IVAAezrgjeugsyVwm/1L4c0bdPEfSXBEotGw/fs/Dy/aVjwkBJekoSjGY6jX0dUKL10MlUGjJbxd8J8fCEEjiUV0dXVAi1rJ1VgsXvNg97GlCl74rv6atteJz3K0GK+5bCO8eoUQiofKh7+AjgbImyq+XDGJiiMuutatW8fkyZOZPHkyIETW5MmTufdeYaFefvnlPPTQQ9x7771MmjSJTZs28fHHH4eEa/Q1ptNlYmJicuSQ5YXNXc14fB4tSCMap0vO6pJEKi0EsFlsAb17f5z9RyZnTY64vSa6gsoLpSNnU2xaEMuMnBkk2hKpaq9ie+12/doMTld6kp0HVj/ASzte4tdf/hpf/kzRC3HKz3q6zN4z5w5RNnjSj8UAZYk1TvR3Sc5+UJQejlVHuhR+qS8K/X54/RpYPIOnW2/lM8cvGb7qVyj4ecVzOrtH3xp4TFcujF4I834NV74CP9sKdx2E6z6CBX+FCx6HO3bBJc+Ic2uphKZy3elqdeP3+WDXx9BWR5WalpjlUkWXdFfm/x4yR0JrFXxwBxSvFT8f3SUWtqkD4dyHAejvF+VmIX1d7fUBf7Z0enh+ZSEAP5k7LEDAnzchlw9un8OEASk0tHVxyysbqG4ODf0IoKtdF4lGmtT7krO1c2TZn2HrGyKCe+cHIiHO7xP9M9nq3LbmMMFi3q7wLpl8nRIzRB9O8Wr49/eFs1W3H6p2wAsXiEW+M1fff7jerPb68OV08hhTrhGz5mp2i/eisUT87F8Gr14FXrfetyhn0xnx+USJY7jkTPn6pRUAfuEKbn8X6otEqemqf8LnfxDb9BsV+RieTpG2F+765HWk5AuB8cIFULJelDZW7xZOz55PwZYghgBDeNHVXCmOEbJ/VUjZ4sUxavcK97F8sxB4ZRuF21i3X3yZoJY2Ux9GPFZ+E/4zJa85c4R4ftFX8PrV4rp7i7dLdw0X/g1s9m43N9E54qJr7ty5+P3+kJ/nnntO2+bWW2+lqKiIzs5OVq9ezcyZMw/7eZlOl4mJicmRw2V3oajf5Dd2NmqiKxqnKyMhI6A8tDvRBTA3fy4AP5vyMxYMXtDttrK8MNjpkn+nOFK0RbndaueUPBGZ/HmxPv8qIDbe2qwlLC4vWc7TO1+Bq98SLtHhYvh8uLsE5twZ+tjk7wGK6O8avVDclz4YcqeIxf72d8V9q58QJW6KlRZrKjV+F21x6XyccB6/9VxP/9QoUsviU0SU/cybYNKVQuDZE/VFctlGTXS5PT461r8Mr14On91LVZNYNGY71Vh6uYBNHyJKm1BE+MfTZ4qfTS+Jx8//O2SNBiCpsworXtYfrKejSxUPX/4v/LlA9KuovLr6II3tXQzJTOKssaH95AMzEnn9R7MYleOkpsXNHf/ZjK+7+V+vfQ/+d7xYTBuRzoorD8ZfIhxGn0c4Qi9dBK9dJcRk1lg49xFwqbPJWoJEl9cj+qSePC2030sGmmSNge+9IYJU9n0Oi6fD3ybDP0+Cun1ikX/9R+r+3KH9QLX74K/D4a0bQ69Pvhc5E+Dip4WI3vIa/L+x4ueF84V7NGQuXPqceu1hBNHGF+GJU2HFI6GPSYGx4K9i3IHPI74EeHQC/G2SKGEF4ayeogaohRNdH/4CFs8ILT30uHUX6uq3hcBtrYJ/nS5KYRdPF6WwFhtc9oIeGhHOTXt+ITx2ihBfAdegunWpA+GadyEpS7iPT5wKj50MT86Fym1ChF/zjkGgBh2juRKeOA2eOy/02FKgFcyB7/1HvN97/yt6AXtL5TbhYManQnbkEUwmoRxx0XW0YjpdJiYmJkcOm8WmRfYbRVc0ThfoYRoAQ1K6TwG8YdwNrLh8BTeMv6HH/WpBGkGiSwZ9SIdOMi9fLzGUpBr6uPY2i4jzBFsCAP/Y9A++Lv+6x/M4ZOxJIkY+mILZwoW69PnAx8fJEsO3RG/WZ2pq3tkP8sTMT5nW+Th/Gvt//I//BnxYyDmUGV25qtNYvokEu5UkdQaXd+fH6v2b9fJCl0NdIKsOnCsP8qfD/PtFGWHqIPGTVgBz7xYL/eQcsMSh+L2Mc7bg9vjYUKS6W/vV/jt1SHSnx8u/vhTi6EenDcFqCV+mGh9n5e9XTiY+zsLy3dU889WByNdXul4I2OBoeClWUvLEa3/uw6L8s98oyB4vXpdR58EVLwtx6lQFYLDT1VgMtXvE4jhYkDUZhF3+DLjyVcgYLgSwPVnMVsoeJxb5aQX63DhjWaK8Bl8XFH4Ven3GYxScAuf8Vezf6hDpdpY4GHE2XP6y7hB1NOpDuyUl6vqrLEyEfoNBsFz4OEy8SjhOcYkioTM+FU79hXjPZSlrOEEkAzyCj9FcDvjF+aYPFcJr4MniGHan2H/qICEqR3xHddwIdbo6GqFml3itKoN62+Q1pORDhnqM/hPFa57UT4iw3Cni/oyheulxsNNVuU3sv/5AqDiW15w6EAaeBHPvEn+Xrg99LaJF9rcNmBb+vyEmEQntEjYxMTExMTk3/VIgAAAgAElEQVQKSHWk0uRuoqGzQe/pcvTsdIEoMfyqVCwII8XFSxRF6XbgspGeyguD93PqgFOxKlZ21++mpLmEAc4BmtNlsyhsqRELy0tHXEqTu4l39r7Dr5b/itfPe53spMNbRh+R1PzQ+8ZeKEIJDq4U5Whet+i/mnEjOWuEg1DW0E5lUx8MRu4/SQRulIm+rkyng9baVhylq8Tj9YVUJoj+uSynQxUEfrGoT1JFwim3i59wWCxC2NQXcmZuF5t3iRLDk4dl6omB1TsBeGtDKZVNneS44rlw8oBuT3t4tpN7zhvDb97exp8/3snMwRmMH5ASuFFnsyhVA7FINqK6Nx8UWTnw+R6+OymP/GveiXzAZCm6gnqujGVmDcWitFMiS+bkfUPmwm0RQiJAuGltNULY5YwPPUZLhSiXjEuIfIzpPxQ/kUjMEP1jDcWQY3i9ZCJlXdDr1NEI8kuPlAGiLPbCx8RPODTRVSycP4vqN/h8+nsQLGSM12CxiIAI6fyFI5IgqjWkEoa831I4qv/ecsbBj5ZHPoYM2Ql27Iwpl3X7IdHw30h5PvL8ssaozwlyWWNBiuEBZiVYrJhOVwTM8kITExOTI4t0jeo762N3utS+Lqfd2adJlJHSC2XgR7DTleJI0XrElpUsE/epoistya7Fyc/sP5PfzPwNI9JGUNdRxx9X/7HPzrlPSBkA+SeJ2/WFYsH/3cWgKOSosfHbyhrx+PxYFOgnAy56Q+4k8bt8E/j9ZCY7GKaUEteh9l51NtHWJG5nueIDF8jRfvOeIha6M9JEwMPKfTVqr5W6EK7agc/n54llYkH7wzmDsdt6XjJdNWMgZ4/Nocvr5/bXNtLpCep5ajSETNQVBjzkVx2ijY1JPPTpbub85QsufXylNgQ6hIhOl0F0NQYFVGguVC5R4VRLGJuCnK5gYScJdh2jQX0vQsSELL9sKAosk5SvYUKaKEntCWcuKFbhBhmdv6ZSUSYX7thGty4aIjldxij4YPFodLqiIZJjZxR2tUHR85rTpYouWaJYtz/2UQMSo9NlEhOm6IqAWV5oYmJicmQxJhhKUROt6Dol7xSGpw3nkhGXREwuPJRzCi4v1JwuR6hjJksMZXS8DNJwJjdT3FyMVbEyNXsq8bZ4fjldzJjaXb+7z865z5Alhihw0ROQJGL4ZSlhpdpn1c/pIM56CMuL7HFikdxSCc3lZCTZOcmyI2ATR1MhoDpdjTEukEFbwI5wiPdtW1kTvhqDY9BWQ2lZMYW1bdhtFq6cET7NMhhFUXjw4vFkJts5UNPKV3uDBjUbRVDQAr2zViz8q5QMTh6agaLA2sJ6bnphHQ1tgXPKAF0QBYuuJqMgCu7/UV2xWEVXd8LOeB3GsrykKL/skGLC+Nq42/SSRk9HoFiS26V07zxqWG3C2YRAcVVneL+DRZe8vmg/U1LUdDQExvDX7jEcL5LTFd1nSxd2UYqurna9L00+N3WQ6EPztMeeSgmifFG+bnlTY3/+CY4pukxMTExMjkqkwCpuLsbjF0ls0QRpgBBHb53/FoumLurTc4pUXihFWHeia13lOho7G5k8MI20xDiG5ItFz7jMcSTFJQF6b9dRycQrRU/ROX8VZWkq/VMCzzkn5RCvISBMYxOZTgezLIFx3cntQmgJp0vGxccgulR3IcVdgc2i4Pb4qC8JFHa1+0W/3eCMJJIc0XdjpCbaOXuccKE+3xkUAR4gugIX4d56cR3OrAJeufEkVt51OiOznTR3enhqRZhyMKdaftqdIAqOYg8u/esJTXR153QZREBvXEfNwTEIn2DHyPi3JrqiFCsQvjTPWJbXWBzo/GjJhVF+phzJev+b8fXorrxQnkvUTpe8hqLAtEWjeDQeT773dqc+fsJq0/djfF60SJcrc8ThGWlxnGOKrgiY5YUmJiYmRxYpcPY3igVnUlwSduuRjSeW5YWtXa10+fQo60hBGgD5rnxGpI3A6/fy+q7XyUtNYP1v59Ovn1gUzciZEdWxvT4vN316E7Nfm639nPXGWWyq2nSolxUd8S4R4jAjMLEuLTEuoPSuv+sQ+rkkhhLDTKPTpc7YyvOLb/D7JTsMC/1YnC6x0LU0FjMwXSQtNpfuDNiko0wEHxRkRpHEGMTpo7IA+HxHVcCMtgCx0lQmZjUB+LzEd4hrKhgyHBBidtF3xMy5Z78qpDZoQLQmiFoqA6PbAwSRQWR4u3SB5oxSdLlidLpiLcuD8KIrONnR6BJpM9midLoCjmEQRMZjeN2hpYcQ23WE6+sylhfWF+piyefVP7fheijDIa/B3aIHZng6IwtJY4iGUQBnDA3dNlrMfq5DwhRdETDLC01MTEyOLFLAHGgUC640x5H/ZlUmKkJgX1ekIA3JDeNEMuKz256lsbMRRYE15Xo/VzSUtZaxqnwVjZ2N2k9Zaxlv7327V9fSVyiGvi7g0JILJTLBsGwjw5RiMpRm3IpDK3HMV6pIT7ILsdcYY58S6O5CYzEFmcJl9FarpWBW0Y9mrRGzleTjsTBrSCYOm4Wyxg52VRqG2QbMUvJrC2Z/cwVWfHj9ChNH63PjvjMmm/F5KbS5vTyxPEiIJGUBCvi9YrByuGMYnbWWSnFMi02k40VDuJ6ujiY9yAKCnK5eiJVwPV3BLoxR2DXEWF4I0Qk7o1iKtbwQAp0oEM5ZQLlfm17u11IpeswUqx6I0hNx8fq2DYXqORfqA6ZBCCkp7ORrJsWgJF0VXb1yuqToMvu5eoMpukxMTExMjkqk6CppFgugaEsLDydWi1WPsjeUGEYK0pCcPfhshqcNp7mrmWe3PUthUyFV7VXYLXYm9psY3cHVtVSCLYF3L3iX35/8ewDWVx5C/HMfYRRah5RcqO1EdbrKNjG0ZSMAO+LGiLImYJBSKfq5wFBeGMsiXIquEgpUp8veoC7Ch4pyUFezWDAPzohddCXYrZw8VPS8BZQYBg+wVRfGRYVC8FWRxqRBei+Uoigsmi+u+YVVhVQ1d+jPtdpEqh7oLo3fH1peKBfhckaXM1dP8OuJcD1dTaWB2wQ4XTGWL0L4ni4piOxqUEZ9GKcrWocIdEFkFFbS6ZHuuVGQxVpeCKFhGs1lonfKYtPFm3TspHB05QUOKO/xGEHXIa8ha6yYh9bVqr9X8npSg0SX5nTFmGDo8+lR86bT1StM0WViYmJiclQiBYzs54o2RONwEy7BsLsgDQCLYuH2ySLC/OUdL/PB/g8AmJw1mXhbbCLFolgYkjKE+YPmo6BQ1FREdVt1zNfRlxiFVp84XTlqmEZrFQPLxKDitf4xWnnhQEuV6OeC3pUXugYACng6GO0SQia1XV2kjhJDZnM6CwF/r5wu0EsMvwgQXepiO1ntx1LFxP69wlVrceSEpCTOHdmPyQNT6ejy8djSIHciOaivq6NRlJ+Ben3tugsWa3Ih6KKrtVqUJ4IuemT/Yb1RrPSmvFAVT2214G4Vt6XoGnyqeoxCfXutvDAW0RXkdPm8upDLnxn4mKdTDEKGQysvrFGd07TB+jwyeV3BcfHREnwd0knLGqWLK3mfdNxCnK7B6rnE6HTV7IbOJjEHrd/o2J5rApiiy8TExMTkKCVYwBwNTheETzDsSXQBnDbgNCb2m0iHt4Ontj4FwIz+0fVzhcNpd2pDoNdXRXa7fH4fi5Yu4oZPbsDtDZOC1wcYywuDgzV6RVyCFqbhrBaDa5e5R2puQn9q6Z9kURfIquCMxemy2bXI9WGOelJowelT38+R5+BHIYVm+tFIQS+cLoB5quhaX1Qv0geNfTwFs8VvVUxUl4rFuJIaushXFIU75ov3+eXVBylvbNcf1Jwo1cWSgiQxQ4+Ub1QX6Jo47R/9RSRmiGHG+PXSOCkY8lW3o7MR2tXh0rLUMxaHKD5F/IDuAElHaOjpgX97u/RQj96UFzaWiPehsUT0cVntMOgU9diF4rd8LW3x4vqjJdjpkuInc7gudKTQizVEQ7uOoBJGeYyMYbqwk/dJ8RfsdGnlhQdii42XpYV5U2Jz50w0TNEVATNIw8TExOTIIsWN5KhxuoISDLu8XbR2iW/ouztHRVH46ZSfAkIIQfQhGpGYmi1im9dXRBZd7+59l8+KPmNNxRq+Lv/6kI4XiT4vLwS9rwto8zv4urOADkcGbks8VsXPMHud7qzY4mNPU1MXvPmWWgYrwinyO3MhKQNPiliojosrI9vVu5ljA9ISGZntxOeHZbur1T4ej3DwBs4SG9UdwOP14Vbj4lOyC8Lu65RhGcwYnI7b4+OXb2zB51NLBrVZXVIQGUotg12R5l44ghaLfoymIGGXOULvDZML/N6UF0LguXZ16MeQoqutRgyWbi4XPUxWu9rTFiXO/qLMz6eGiUiXJ61AF0TydTL2CMYybsKYkGjs58oYpjm0mnjsrdMVqbzQKLrktRmDNIyk5Ash7e0MHC/QE5roMqPie4spuiJgBmmYmJiYHFmOWqfLHuh0SfFlUSwBQRvhmJ4znVn9xYI70ZbI2Myxh3QumuiK4HS1uFt4dMOj2t9LDi45pONFwii0snopUkKQCYbABv8IurBR0+qm2iacmgJrdeCMrljnsakL3vSuSoZbhejqTBGL44Zk4QbMSK48pDlv0u36fGdVYB+PHFJbX8i2sibSfaIEMCN3SNj9KIrCHy4YR3ychRV7avQI+RCnyzBwVwuoUO/rrSAKOYZ0swYEOi/eLt0Ni0XYgR7/3nhQFQt+EXWePgQS1H/39YWBr2G0fWkgnBl5Tg0HdbGSPlQXJZpw7EWJJIjXQ7EKMdNSoZcXZgwzvN9BPV2H6nTVGa7DmErY0aS7j8HlhVab7soFh4l0hzYU2TQjeospukxMTExMjkqCkwCPFqfL5XABuuiq7xCLmxR7Chal5/+tLpq2iOS4ZM4bch5xlrhDOpcpWVMA2FO/J2RgM8CTW56ktqNWmwO2tHgpXmO8eB+RlyrCKPo5HThs1r7ZaX9ddG2LGw9ATYubUkQfU66vsneBBxJ1wWtpKmZiohA99fFiAV4aVwDAuLheDJA1IPu6lu2uxmdM3dPKzQr5ak81uYqIALd0UzI3ItvJvecJkf7XT3axubghdFaXMXVPuigNQeWFTr28cOW+Gs7+3+W8vyVoDpcRzU0LcrpS8gNL6oyDkROjHIwsMTpdUgikDxZC2vBa9SouvrtjZAzVhUxTKXg9vRdd1jj9c1hfpA9GNpYXak5XL8JAQBdQDQeFsJLvScaQwPJC+Z4npIMjzBdBscbGdzZD1XZx20wu7DWm6DIxMTExOSpxWB0Bw4KPhsh4CO3pkv1cweWQkRiVPorlVyznnln3HPK5ZCRkMFh1ZzZUbgh4rKipiBd3vAjAA7MfwGV3UddRx6bqvp/rNS7Pxa3zhnH/+Yfm3AWQM06UhAH7k0SpYW1LJwe8oqQtw1Oml0fFukAGgygpZmSccGhKrcIF2uMXi/rB/oNhnxotUwamkpIQR0NbF2VFu/XjpuQLV8TTzo49e+iv1IrHehCPV87I55zxOXh8fm57dSNtDrW8Ty6+m4wuVFAqYJCY2FbayE0vrGdnRTNPLOvG8ZDOWIibNiCw3M0o6mJxoSDgvdBdKNUd0lyZA4ayvBgGI2vHMAgW4zGcOaLczucR19ibvjSJPNfqnbqblTFcv7+9DtobAh3JWHDliZRCrxuKVor7EjNFaW2GoVdLispgl0ui9XVF6XTtXwr4hSPpjDLi3iQEU3SZmJiYmBy1GEsMj7ryQneg6OouRCOYQ3W4jMgSww1VgaLrobUP4fF5mJ03m9MHns5pA04DDk+JoaIo3HnWSBaMjyGkoSfiEuDsB+Hk26hJnQBAdXMnu9wi3MDVXhJYXhgrKbooyfcJwbDHIxaUmzrE76z2Qj1yvRfYrBZOGyGEUVWJutBPGaC6IkLYNZZsJwvxGRKpipFRFIU/XTiBvNQEDta18cQGNVSjJUxPl7y+hmLRYyTdMFcuxXVtXPvsWlo6RTLo1tLGwDh6I8aeLp8vMC1SFTI1Jbv5x7vLACgnnWW7q2l3x+CohnW6pOgyOl29mNEVcozCQKfLYjWIvqLeO12gC7v9XwB+cKRAUqZwm2T/W9lGPWEy1uuwxumfkX2fq9egOlyuAWLGnK8LCr8MPJ9gMtTXNhqnq2IrvHOLuD3irNjO1yQAU3SZmJiYmBy1GIXM0VJeKB0tGRnf02Dkw43W12WY17W8ZDlLS5ZiU2z8YvovADhj4BkAfH7wc/yHICS+VWbcCN/5AxlO4Xjur2llv+p0xTcXH1p5oaH8LtMtFvNbOsS+VzWm4/Ur2D1NgTOqeoEsMXTXycQ6ddGsuh+TfDuwKH78lriohhanJMbxyGVittvru9QY95ZKPZUPhINiFDJtNcIdQaFWSeOaZ9ZQ09LJqBwnI7NF+dmyXRHGDjgNTldrlTrU1yIcLdVJaa86QEOF6DNaU5vAD55Zw9VPr47i1ZEXZSiFNAoiMJQwHuib8sK6A3rCoHR8jK/VoYguea77lorfmcP0XkMpIg8sF7+T+okvFmI+hiqkgkWXxaK/ZvvUL1YiOYLRDkiu3QcvXiQSKgfOgvn3x36+Jhqm6IqAmV5oYmJicuQ5mkWXVl7Yw2Dkw820bNFjsb12O21dbVS0VvDbL38LwFWjr2JIiljsnZx3MvHWeEpbStldv/uInGtvyUgW4Rzby5o46Bd9TJaGokMrL5QL/c4mbN4OPH4L6xqcdHq8FDZ6KfSrDo/sZeklc4Znoijg6qwMPK7a53OSZQcAiiv6ocUzBqfjdNio9LnwKxaR6NdcHihCpTBxG/pxkrO49d/bOFDTSl5qAs9fP4OzxorXc2lE0WXo6ZKix5krAhlUJyXLW0meIvriHOni+jYWN+D2RBlJLsVBaxVUiddDEylhe7piLMszHqN0vRCOtnj9c2MM0+iL8kLZX5kx3PCYeh1SdPXmGsAwj0sGdRjCV7ReLTU5MVJ5odyuvlCI9XA0lcOLF4j3JHs8XPka2BN7d84mgCm6ImKmF5qYmJgceaSQSbAlBPR3HUmCI+Ol03Wkes5yknLITcrF6/eyrnIddyy9g/rOekanj+a2ybdp2yXYEpiVK5ITI5UYtna18psvf8PdK+7mHxv/wdt73j4qBFpmsh2A7eVNlPoz8aEIMVGtnltvRJcjOSBm/qA/iwP1bgpr2vD5Yb+iLoqrdx7SuWckO5iQl0KuKkp0p0sswqdY9gTeHwWKojA8OxkfFjod6iyp8s3g94o+uORssUCWztlB4Tp5kvuzar/oH3v++ulku+KZqzpxy/dU4/GGEUlaT1dFaHlfygD8ihWH0sUUq3Cozpo1hWSHDa/PT1Fta3QXlJAG9mRxu0V1FoN7uhoO9n6+FegCxKOWUaYN1kWuFDI1u4UrCIfmdEkyh+m3pXgsU8uAYw3R0I4RJKQyhoW/DZAadD4SWYrodevvqZGWKiG4Gg6K9+HqtyDhyHypdDxhii4TExMTk6MWKXCOlhANCI2MjzVI43AgSwzv+eoettRswWl38vDch4m3Bc7MkiWGkUTXZ0Wf8d6+93h///s8seUJ7l15Lxe/d/ERF179nMLpqmt104mdeqsqNLyd4ndvXAkIWLwX0R+Pz8+Xe8WiuyZBXfRL5+UQOHNoEqmKKkDUxXyVGn2foLgD7o+WEWpZYIN8LWSktytX9CmBfn3FYj5bs10IrNyUeIZliedPHJBKWmIczR0eNhxsCD2QdLo6m6B6l7pf9VytcbTFi8fHKuqA55Q8hvYTaZn7qluiuxhFCSyFi0sUwhFUV80ugi662gKPHwtyVpdEuj2gi66D6hw7W0Lsc9+M+9GOYRBB0ulSZ/QdstMV7hjBoiuS02Wx6CIwuK+ruRKeO0982eDMhavfhuQYZqKZRMQUXSYmJiYmRy2yT+poCdEAPTK+2d2M1+fVna4jWP4oRVddh4gef3DOg+Q7Qxd1c/PnYlWs7K7fTXFz6DfcpS2itGpcxjguGXEJmQki+ntn3aG5PYdKRlLg7K96h8EVikuE3vbTGRb6dWpc/NJdVQC0pamlYYfodAGc3l8IqyaS8MQJR2dlnStwoxiFhBRdVX712uXwWuNiXl5fsXisWhH/joZl6zHiVouihX18oV57AA6nmJkFurAzuHJVNiG6bKhlaq48hvYT17ivOkqny3iuINwV2QtlsQQKjd72QlmsgW5iuqEsTx672VCe2Zv5bEmZoI5nAALLC6XIkfRadAX1aRmvI31o4GPdHSNcgmFzBTx/HtTsEl8CXPt+qHtn0mtM0WViYmJictQiHa70hKNHdEmny4+flq6Wo8rpArhpwk2cOuDUsNulOFK0HrDPD34e8nhZi1h0zhs4j/tm3cecvDmALsa6o8XdgtvrjvncoyHTaQ/4uy3JsHjuzWBkiWFR2u4Si+LV+4VwtWaNEQ9U7YCO0BlosTAqQTy/1JfB5hLxefmgJGiIdIxO18gcIYSK3Ornrmyj+G0UFrKEzd0MQLFH/HsakZUcsC85xPmLnWFEF+huVxhhV+jNCNzWlcdQdf/7qqJ0uoL2GSJQjH/3JkRDYhQsRqcr2BHqTWkhiM+hcV/GYxjFEfRNeaFrQKAANTpdyTkQF+h0BxCcYNhYIhyumt1iv9e+H3j+JofMCSG6Dhw4wLx58xgzZgzjx4+ntTWGb15MTExMTI4YZww8g1MHnMpVo6460qeiEWeNI9EmGsobOxu1II0jWQI5yDWIH4z5Ad8b/T1+MvEn3W4rBVnwXC+AilbRT9M/SZS+9U8Wv8tbuh8SXNNew5lvnMnVH119WIRXZnKgQOlyGhaevS0thICFr5IpXAm32tfkHDBGfMvvboGP7up+P3v+Cw8MgGV/DfuwtVkEQJT6M1i6q5rmji6WFnVQ5zeInxjFxPBsVdh0qPuQMeRGwZAS6IrsbncGPFdy6vB+KArsrGimvLE99GAudRSA+lmX5+r3+9nWZvjcqwmMMZcXQqjTZcTotvSV6DK6QklZosdJ0lvRBfq5puQHCqLEDN0xlI/3huQc/VyDRVFSpoiph8ilhRJjgmHRKnhyrgjnSMkXgiv4PfiWeXXNQZ796sCxk7QaBSeE6Lr22mu5//772b59O8uWLcPhcPT8JBMTExOTI052UjaLz1jMKXmnHOlTCcCYYNibOV19jaIo3Dn9Tu6acRdW2c8TATlMuaSlJOQx6XTlJovwhNwk8bustazbfa4pX0NrVyvba7fz5JYnu912ecly5r8xn2XFy7rdzkhaoh2LwcxSMgzORw+zrbrFsPBNyh0Z8NCgfi644HFAgc2vwPb3wu+jqwM+WCTcpC/+AGv/FbpNoxRdmSzdVc2Xe2ro8vqpshrmmsW40O+X7CAtMY4Kf5DYD3C6AkXX1iYhhoYbygsB0pLsTM4Xn9+wKYbOoPlr6rmWNrSz121wulxiMLKxvDDqRbPR+QkRXUanqxeDkbVjRHChLJbA1+qQhLx6jOD+KkWB9ALDdr0UXRaL/txwx5DXFWlGl0RuV7QKnl8IrdUipfC6D0Odxm+ZulY3v357K7//v+38c2kUs8SOEY570fXNN98QFxfHnDmiRCI9PR2bzdbDs0xMTExMTCIjRVddRx1NbjGv60jN6YoV2etV0lwSsCD2+X1UtAmnS4otKb56crq21mzVbj+99Wl21e2KuO1/i/5LRWsFv1v1O1rc0TkhVotCepJeYhifZViUy3S93iDdgLgksnILAh4qyEyCQbNg9s/EHf/3UxEyEMzqx8VQXek+fHBnqEBTRVeZP5OtpY28vk7003mN6XIxii6RYOjUe7okAT1dgQv77a1CDA0LKi8EmDeymxLDYNGlCrtvypoo9htCFtRrGJiRiNWi0NLpoaq5M5rLOWxO15Idlfz2na00d3Tpx7AlhF6T8fiH4nQNOln8Lpgd+pgUj3ZnTH2Ibo+P/3l/O+9tLgvcT+bw0I3lfT31Ykmny90sIvTHXAA3fBJ5tlcE9la1cPdbW/lse5h/G71ke1mTNpP8r5/s4v0t3X/pc6xwxEXX8uXLWbhwIbm5uSiKwjvvvBOyzeLFiykoKCA+Pp6ZM2eyZs2aqPe/Z88ekpOTWbhwIVOmTOGBBx7oy9M3MTExMTkBkX1dxjAKl90VafOjitzkXBQU2jxt1HfWa/fXtNfg8XmwKlb6JfbTtgUoby3H5488c+mb2m8AEXji8Xu456t78Pg8Ybetaa/Rfj+++fGoz9tYYujsb1hsHoorkTMBZt0KC/7M4H66EHE6bGRIkTf318IBaK+D924Fo3PTUgXLHxK3Fz4KU68F/PDmD6Fopb6dKrqUVCEYvlDdJFeueh22eEiMvW9xZLaTyu6crqAStgp/Ov1T4nHFx4XsS/Z1fbW3hk5P0Owmo0CJS9KS/baHiC7xeXHYrAxMFyW4Ufd1pXQjug6hp+u+977hpa8P8r//3QM548WduZNC+wAPQXS9tuYgjy/bh8/nhzHnwx27Yc4doRvK60jNj6kP8YOtZTz95QHuenMLbW6P2PfEq2D8paEbz7oVJl4JU67G5/Pz2NJ9/OmjHawvqhPnJ3H2VxMiFTj9Hrj0ObAnhe4vAh1dXh75bDfnPLqCV9ccZNHrm2jpDP9vPla2l4seyPg4IVMWvb6Z9UX13T3lmOCIi67W1lYmTpzI4sWLwz7+73//m0WLFnHfffexYcMGJk6cyFlnnUVVlf5NzKRJkxg3blzIT1lZGR6PhxUrVvDPf/6TVatW8dlnn/HZZ599W5dnYmJiYnIcIhMMi5qKAHDandgsx0YVhd1qJztJxHGXNOslhrK0MCsxS7uWrMQsLIqFLl8Xte21Yffn8XnYUSti1R867SFcdhc76nbw3DfPhd2+tkPfz8s7XmZfQ3TlQxnJutOV2S9X7485lPJCRYGz/ghTribbGa8t8goyk1Dkothmh4ueFE7Wnk/h/Z9Bh9GmcNEAACAASURBVHA3+eKPwinInQwTLodzHoaR54oo+1ev0OPm1VlIAwpGaId2Omz0HzxavYbehYGMyE6mKkR0GQRDvEtzVDrjUujAEdblAhjT30VmsoNWt5fNxUHBIS6D6EoZoJ3r9vImqknBY4nXr0Ml5r6upExVSFwGrjyaO7p45ssD1LZ0BpbKxVCWV1zXRkm96FF7YVUhB6wFcMNncOnzAByoaeX5lYV0eX2BPVBhhPzSXVWs3h/6b6C8sZ273trKgx/t5N73tgn32Jkd/v3sp77fMQZUvLVBBNm0ub188k2FcGAvfEy8ZsCn31TwlTrqgP4T4MLH8afkc//72/nzxzt5Ytl+Ln5sFSf9aQn3vbuNula3KFO8/mP48Qo49c6YPn+bihtY8OgK/rZkD26vD7vVQnOHh3+vDTPzqxdsLxP/vm4+bRhnjs7C7fFx0wvrOFjb1if7P1IccdG1YMEC/vCHP3DhhReGffyRRx7hxhtv5LrrrmPMmDE8/vjjJCYm8swzz2jbbNq0iW3btoX85ObmkpeXx7Rp08jPz8fhcHDOOeewadOmiOfT2dlJU1NTwI+JiYmJiYkRWV54sFkMaz2a5ohFw4BkIVSMTl15qyghlCEaAHGWOLIShZMRqa9rX8M+OrwdJMclMzV7Kr+a8SsAHtv0mCZKjUjxNsg1CI/fw59W/ymqvh9XUifx/f+NM6WEBIcNRp0r4sNzJ0dzyT1isSgUZAihUJAZ9I1/9hghzgDWPweLZ8DKv8OGF8R9Z/1JLGKtNrjkacifKRIPX7pYDJhtEq/d2FFjtF2eOrIftiGngsMFIxf06pxHZDupxYVHLuccLogPStFUHZwGm1igD88K7OcyXv+0QeJzvOFgkKtgdLoMgkQsjhXcTlX4BoiuGGPjFUUIiYufAkXhrje3cv/72/nVm1vFoOehZwjx1W9UdPsDVh+o0253ef088OEOyJ8BzmyK69q49PGVqhNW1K3TVdPSyQ+fX8fVT68RgsXAR1srtNsvfX2QP320M+DzXNrQrouFsRfC2X+G+feHPd+9Vc20uwNdxorGDl1QoQsw7Rr313LTi+v53r9Wc/dbW7Tn//WTXTy3shCAM0Zl4XTYqGru5PlVRdz26gZxjulDdPcvSjo9Xn704joO1LSS5XTwz+9N4b7zxef6mS8PhB+wHYHiujaqw5Sfbi8Xa+/xA1w8esVkxua6qG11s+j1Tcd0sMYRF13d4Xa7Wb9+PWeeeaZ2n8Vi4cwzz2TVqlVR7WP69OlUVVVRX1+Pz+dj+fLljB49OuL2f/rTn0hJSdF+8vN72ehoYmJiYnLcIssLpag4kiEavWGAukgO53TJxEKJFqbREl50yX6usRljsSgWFg5ZyPSc6bh97pAhzH6/X3O6fjfrd9gtdlZXrOaTok96POca63+JS92IPVPd50VPwKKdkJTR/RNjYLAqtgZnJIY+OONGuOZdsVBtLodPfysG3Y65QDgPkrgEuPI1yBwJTaXw7LlisK9iZdyokTgdwkU8Y1SW6Lv55QFd0MXIiGwnPizU+FWhFa70ThUTFf509TnhnS6AKYPE5ziklMsZ5HQBDW1uShuEi2QbdJJ4LG+KtpkWGx9LgqHK5zsr+WCr+BLgvzsq2VHeBN9/E27fGNOMrq9VZ2r+mGysFoXPtleycl8NDW1urn12DTUtQkC9sb4EZH+dPTlEuO6ubMbj8+P2+nhvU6Do+VA9z5OHis/hk8v388hnu3lzfQlXPLmKUx78nDMfWSauIS4eTvpx2GTALSUNnPnIcq55ZnVAGeC7m0rx+fXP5ld7a6hs6tAeX2wImnh1TTEL//Elv3vvGy2A4g8XjOPpa6ez7p4zeeqaaThsFr7aW8s7m3oeAxGOtzaUUtnUSY4rnv/ecRrnjO/PxVMGkJ5kp7ShnY+/qeh5J0BLp4f5/28ZFyz+Cq/heju6vJpQH9M/hSSHjWeunc5JQ9L58yUTdAf6GOSoFl01NTV4vV6ys7MD7s/OzqaiIro31Waz8cADD3DqqacyYcIEhg8fznnnnRdx+7vvvpvGxkYeeughRo4cybBhwyJua2JiYmJyYiKdLilEjpUQDYl0uowJhtLpkiJLIkVYJNG1rWYbAOMyxwEi4GF8pvj2vLotMAmvyd2k9XpN6DeBG8bfAMDD6x7G6wvqIwqi0rMeAH+cYZ/W8CWdf9/4d+a/MV+LwI+W604ZzLyR/bhoSoSSxSFz4eaVMOdOsNjEAn3+70O3S0wXIsHZHxqFG4orj7i4OO5ZOIaLpuRxzvj+3V5DNKQl2enndOh9XSkD6PL6uP65tdz80nqxeFdF1wG3+IwGx8UbmTJQ7GfjwfpARyHZsA5T+8SkG5GfnoD9u4/Cz78RLpKK5nQZero6PV6ufXYNd725JeI5tLk93POO6BFMVgXq4i/2Ciesh2TOYKTo+v5Jg7hqhngd/uf9Hdz04nr2VbeS44onzqrwTVkTOy1DYMIVMPfukFI7o1v3psFpqmjsYJ0qUB+5bBL3nCccn79/vpc7/rOZr9WZb26vjz98sL1bl2aN6sqtLazXAjP8fr/mbN04ZwjTBqXh8wshBrCttJHlu6uxKPCXSyaQ5XSwt6pFc7h+c85ovn+SKJt02KzMH5PN7WeIPsI/vL+DhjbdtftwazmnPPg54+/7RPs559EVAU6U1+fniWVCzP1wzmCtNzA+zqod56kVesz7ropmzv/Hlzz4UeiA8YY2Nx1dPkob2rVyQhAC1+vzk55kJ9sl+jizXfG8dtMs7TN1rHJUi66+YsGCBWzdupVt27bxyCOPdLutw+HA5XJxxx13sHPnTtavX/8tnaWJiYmJybGCFF1+xOLieHC6tPLCCE6XfDyYYNEFaCWJVW2BSXiytNBpd2K32rl+3PXEW+OpaK0IKHUM5mDTQeq7xONdSm2Ps8De3vM2Fa0VMcXSA8wYnM6z180ILS80EpcAZ9wDP9sKt6yOnBKXmi+ElyPQhbpsWj6PXDaJ+LjYBEQkRmY79b6ulAG8ub6Ez3dW8dG2ClFeN+l7eAbP49l2keI8LEJ5IcC4vBTirAo1LW6K6wzzumx2UcppuA65UB7T3yWEY5DLJnu6yho7aFUDFj79ppKlu6p5bW1x2LIygEf/u4fShnbyUhN4/noh4j7YWs7+GB0z2c9lU8smfz5/BM54GzvKm1hzoA6nw8Zz10/ndDVA5M2N5cI9PfnWkH0ZhePW0kZ2VYhh0x9tE/8mpg1KIyclnhtmD+YXZ4nRA4MyErnzOyN4/UezsFuFu7RkR4Th08CeSv0Yf/54J+1uL9vLm9hV2YzdauHc8f21LwPeXF+K3y9CMgAWTszlsmn5fPTTOZwxKgtFgUXzR3DjqaGO2o1zhjA8K5naVjcPqqWQTy3fz09e3kBpQzvNnR7tZ3t5E794Y7PmvH24tZzC2jZSE+O4ckZgyuE1swZht1nYXNzAuqJ6vtpbwyWPrWRLSaMmEiPx1T69fNL4uTqWXa1wHNWiKzMzE6vVSmVlYAxlZWUlOTk5h/XYixcvZsyYMUyfPv2wHsfExMTE5NhDlhdKjlnR1RKmvDApSHQlRy4vbPe0s7dhLxAouvoliAV6dXug0yVLCzMTRH9RvC1emxt2oPFAxPP9ovgLw1/+bgVaTXuNdtyd9aHfsPcZrtyek/Syx8KVr0LmCJh4xWE5jeHZyez1i/fIkzmKv3++V3vsP+uLIWccW+Y9y2b/MLJdDlISQpMLJfFxVsbmis92SF+X7KVSf+uL46AeMpXURDuZavjJgZpW9Xz0z1vI/tV9/utL8Tm4/7tjmToojTNGZeH3owmMaJH9XBMGiBK19CQ7P1VdnjirwhNXT2VUjotLpgrn7u2NZRH7kWSJpMMmls1vbhDXIUsLNdcSuGXeMDbeM5+ld87l1tOHM2NwOtfPFp/xBz7cgdsT/hh7qoSQUxQob+zgqRX7eVt1uc4ck0VKYhznju+P3WphV2UzH26t4ENV9N08VwRzZCQ7ePra6Wy57zuaoxWM3WbhgYuEE/3a2mJ+9OJ6/vihCHy59uQClt45l6V3zuXVG0/CYbOwdFc1z64sxO/3ayWL155cQJIj0KHNTHZw8RTRC3fXm1v4wTNraI4yzdDYsyYd1DG5x0YabCwc1aLLbrczdepUlizRa8J9Ph9Llixh1qxZ3Tzz0LnlllvYvn07a9euPazHMTExMTE59pDphZJjTnSp5YWVrZWaayRL8YLLC7tzunbW7cTr95KZkEl2ol6CFsnpknHxGfF6H1ZBSgEA+xv3RzzfpcVLA/4OF9Ah2V23W7vd3bywb42CU+DWtTD1B4dl9yOznfzDcwEPZf4Pr/tOp7ShnUS7cNE+2lpBS6eHvaqLMiI7ssslkSWGIaLooifh6ne0vi25OB7bzeJ4iFoOtreqhfLGdlbs0UV4cN+Y3+/nN+9sxevzs2BcDmeMFp+nW04XbR5vbyylpD769LpV+4TAP2mI/ln7wckF3PmdETz9g+mcPEwI/7kj+5GRZKempZMVe2rC7ks6XT84uUA7l7KGdq20cMH4QCMgLcke4NLcMm8omcl29te0itCOIPx+v+Z03TJXXO9jS/fx9kYhui6cLP69piTGccZo8W/rjv9swu8XvYGjcgLfA2eYkQBGphekc8V0ITY/3V6JosBvzx3NfQvHUJCZREFmErOGZvDbc0UGwp8/2sljy/axo7yJRLuVa9XXIZgbZgtnbV91Kx6fnwkDwgvyYNYW1mljCgIc1OOMIy66Wlpa2LRpk5YoeODAATZt2sTBg6IGetGiRTz11FM8//zz7Nixg5tvvpnW1lauu+66w3peptNlYmJiYhIJWV4oOdZ6utLj00m0JeLHT1lLGU3uJlq6xKIvJylwAWns6QruSTGWFhoXmXLOV3VbdcBzZHlhRoK+EB6SIhZqkURXQ0cDG6o2ADCx30Sge9FldLd21++OOC/seGF4tpNWEnitYQx/XybWTr88ayRD+iXR3uXlgy1l7K4ULkqkuHgjMkwjRHS5cmHoPECEHexRhUh3joSeYNjCWxtK8fuFywShomtfdQsbDzZgt1m4b+FY/XwGpnHy0Aw8Pj9PLo8szIOR/VxG0RVntXDr6cM5dUS/gPvOnyS+WHhjQwnBtHZ6KGsUwRU/nDOYtMQ4qps7+e072/D7YcrAVPqndB/u4YyPY9F8UXb46JI9Ab1UAJVNnTR3erBaFG49fRhTBqbS3uWlttVNepKd0wznK0sMO7qEY/aTebHFz0vuWjCK3JR4HDYLi6+awg/nDAkp5/v+SYM4c3Q2bq+Pv3wsvsC4asZAUhPt4XbJsKxkvqu+lj8+bSh/uGBc2O2C6ejysfFgAz6fXwSOYDpdh4V169YxefJkJk8Wka+LFi1i8uTJ3HvvvQBcfvnlPPTQQ9x7771MmjSJTZs28fHHH4eEa/Q1ptNlYmJiYhKJY728UFGUgBLD8hbhYqU6UkmMC0zuk+WGbZ42mtyBY1RkcuG4jMDFlSwvdPvcNHbqM59keaHR6ZKiq7CxMOy5Li9djs/vY0TaCGbliiqXbkVXnS66Or2dHGw6GHHb4wGZRljT0kl5Ywf9U+K5YsZALpkq3t//rCvRBFKkuHgj0unaUd4sBvEG0enx8tjSfXh9flIT4+ifEh9xX7Kva29VC/9ZJ0pCb1L7jLaWNAYMYV6qDoyeOTidnKB93jpPuD+vrS2mqrmDniiua6O0QfRzTR3U8ziHi1Uh89n2ShrbugIek6WRGUl2spzxfHeSKKH7fKdwcY2lhd1x+fR8RuU4aWzvCimVlKWFgzISiY+zaoEcAAsn9Mdu05frp43oR1qicLJmDk5n6qDYh2qDKP/8+OensubXZ0a8BkVR+MslE7RAC7vVwg/nhPaJGXn40oms/vUZ3LVgFJYYerJW7q3hYF0brW4vDpuFId31VR6jHHHRNXfuXPx+f8jPc889p21z6623UlRURGdnJ6tXr2bmzJlH7oRNTExMTE54QpyuY0x0QeCsrnAzuiTxtnjS48XCLriv65sakTIn0woldqtdm11W1a6XGEqnS/Z0AVpP1/7G/WHT3WRp4bz8eQxyiYS07kSXLCm0KaLnxCjCjkec8XHkGkTKLfOGER9n5eIpA7AosK6onnWFor+pu7h4SW5qAjmueLw+P1tKdMHs9/v57/ZKzvp/y3l0yR4ALpiU123YgYyN/2JXFYW1bSTardw8dxgZSXbcXh/bSnURv2y3EF1GV0cya2gGkwem4vb4eHpF5N4/iXS5ZD9XT4zNdTEqx4nb4+P9rYGfcdnPJV27i4OSLRdEKbqsFkXrs/rvjsCsgt2y/FMVxZMHpnHtyQWkJMRx9ayCgG3tNgs/Om0ozngbvzx7ZFTHjoQrPo6UxO5LEdOT7Pzv5ZNxOmzceOrgEEEcjM1qIdvV/Tbh+GpfrVayOirHic16xCVKn3P8XVEfYZYXmpiYmJhEIt4Wj8Pq0P4+JkWXIcFQiikZmhFMXrL4dt8ouho7G7Xh0GMzx4Y8x1hiKNF6ugzlhYNcg7AoFlq6WrTHJZ3eTr4s/RKAeQPnMcjZvehq97RT2FQIwKkDTgUOc5jGUcKIHLFYz0tN4LJpolcn2xWvCZhWdWBuNE4XhC8x/M072/jhC+sorG2jn9PBQ5dO5F6DIxOOYapQkaVw547vT7LDxhQ5hFktMWxze1itxqvPHZkVsh9FUTS366WviwLK8/x+P3e9uYUzH1nGElXMyKh2Y2lhdyiKoompN9cHlhjKfq6hWcJ5GZfn0sTrpPxU8lKjnxs2Sz2ffdWt1Lbo6Y17VafLGOd/38IxbL7vO2FLQn982lC2/u6sXrtcsTJraAZbfvcdfnFW9IOpY2VzcYMWm388lhaCKboiYpYXmpiYmJh0h7HE8FgXXd05Xcb7y1p10SVdroHOgSHOH+iiyximEa680G61a65bcF/X6vLVtHvayUrMYkz6GAa6REx1dXs1rV2tBLO3fi8+v4+M+AxmD5gNHCVhGoeZs8bmYLMo/Pqc0QGlaJeqAgwgy+no0dWQaGEaRQ0AfLClnFdWH8SiwI9OG8IXd87lkqkDsFi6Lx/LTU3QEv+M5yNL/mRf19f7a3F7feSlJmglicGcPiqL0f1dtLq9PPtVoXb/6+uKeW1tMXurWrjh+XXc8fpmVqoR5NGKLkDr69pY3EBdqy7q5Iwu6XQpisKPTxN9VNedUhD1/kEEbAxXRZSxp006XUaBdbTFpR+u84mPszAwPRGPzy+GVHN8hmiAKboiYjpdJiYmJibdYUwwPCZFl2FAck+iK1xsvOznCudyAWQlCMfCGBsfLkgDIodpGEsLFUUhxZGilTqGc7ukqzUqfRSj0sS38jvrdnY7lPZ44MoZA9l+/9mcOyHw/TtjdBapqtDqbihyMJMNQ5Krmjr47Tvivb5l3jDuXjBaG1rcE1aLwmC1N6cgI5HpBWK/muhShzDLfq65I/tFXNwrisItamjEcysLaen0UFzXxv3/tx0Q/U2KIuLcyxs7xHyugp77uSTZrnhG5Tjx+wMjzIPLC0GEWez+wwKtvysWphWIz69MPhTJhcLpiiZd8njklGHivwctasS86XSdYJhOl4mJiYlJd0h3JykuiThrdA7C0USA06UGaUQqL5RizBgbv7F6IxAaoiEJdrr8fn/InC7J4NTQWV1+v18bbjwvf552v+zrCheQIV2tkekjGZY2DItioa6jLqRs8XjE6HBJHDYrF6lx4+Pzov9iYFyeC7vVQm2rmxtfWEd9Wxdjc13cdnr42U/d70v8O7lser4mqMarQ5irmzspqW/vtp/LyIJx/RnSL4nG9i5eWFXIL97YTKvby/SCNF658STe+PEsTeRNGZRGoj06cSiZM1x8Lr9Uo+O9Pj/7awKdLkm41zsapPBcq/bZVTd30tThwaKgnfuJxslD9f8eKAqMzDFFl4mJiYmJiYmKLC88Fl0uEAJLQaHN08buejHbSsbDh9sWdKerqq2Kr8u+BmB23uywz9GcLrWnq8ndpMW3S7dKMtilh2lIdtXvoqq9igRbAtNz9KqTgU5RYih7t4zI0IxR6aNIsCVQ4CoIuD8cq8pW8U3tNxEfP9b55dkj+cslE2KKFnfYrIzLEwvfzSWN2K0WHr5sYq+Exi/PHsnDl07kJkPqnXEI8xvrSyiqbSPOqmizsyJhtSjcrJb2Pfzpbr7eX0ei3cpDl07EalGYOiidD2+fw4MXjecvF0+I+VxnDxeib8UeMeqgtL4dt8eH3WYhLy363q3umK46XdtKG2l3e7XSwoKMJOLjrH1yjGONk4ca5vZlJEXtpB5rmKLLxMTExMSkF0inqy9Fl8K318fhsDq0IcYdXhHD3VNPl3S63tv3Hl6/l8lZkxmSGj5COtjpkqWFTrsTuzVwzo/ch9HpkgEaM3NmBmwvhykHlxd6fV5NPI5MHxnwe1d9+L6ukuYSbvrsJq54/wp+tfxXVLZWht3uWCY+zspl0/Jx9TAwNxjZ1wXw8/kjQgbwRkuWM56Lpw4ISaOTJYZPfyne82mD0qNabF8wOY+81AS8PlEy+utzRjMoQ3eIEuxWrpgxkIJeuEYzCtKxWy2UNXawv6aVvdWi7G9IZhLWHvrXomVAWgLZLgddXj+bSxq0uPhoZqgdr2QkOxit9nEdr/1cYIquiJg9XSYmJiYm3aGJrm9pMLKfvu9LynfqQQvx1ngt5j0Y6XQ1dDbQ2tXKW3veAuCi4RdF3LcUdDIyPlyIhkTGxle1VdHiFt/8S9F1St4pAdtGKi8sbi6m3dNOvDVeSzkcla73dYVjR90O7faHBz5k4TsLeWrLU8f9QOVokCmC0wvStNlafYkUXbKPZ+7I7ksLJXFWC7efIZIMTxvRj+/NHNhn55RgtzJ9sDivFbur2VcVvrTwUFAURe/rKqzT4+JP0H4uyTnjxFD2U3pwO49ljk//rg+45ZZbuOWWW2hqaiIlJTSVycTExMTkxCYtXizOwomIw0lfumEDnANYV7kOEKWFkUIMnHYnTruTZncz7+59l+LmYpLikvjOoO9E3LcUXbXttXh9Xq2vKrifC8Bld5GZkElNew0HGg9QkFLA5qrNQKjokuWFB5oO4Pf7tXOWIRoj0kZgtYgyLRmmESnBcG/DXgCm50yny9vFpupN/G3j30iPT+fiERdHvLYTgdnDM3n/ttkMy0ruM5fHSPDQ4tOiFF0Al03LZ1SOi1H9nX2eqjd7WD++2lvLl3tryEwWYyEiJSr2lumD0vhgSzlrC+u1AdSxBJ0cj/xk3jDmjcoynS4TExMTExOTQM4ZfA7nDz2f743+3pE+lV4jEwwhcmmhJDdJuF3/2vovQFx/YlxixO3T49OxKBa8fi/1nfURkwslMsHwQNMBVpevxuP3UOAqCHDjAC02vtndTENng3a/MURDMiJ9BCBKEdu62kKOub9B9JDNyZvDCwteYG7+XAAa3Y0h256IjMtLOWx9RtmueAaofVI5rnhGxuD0KIrCxPxUHLa+PzcZprFqXy07K0Tp39A+Lv2TTteGovqwcfEnIlaLwri8lB7HEBzLmKLLxMTExMSkF+Qk5fDH2X9kTEb3A2KPZmSCIfQsumTIhoyAv3h4906QzWLTXMCqtqpuywtBLzHc37A/YmkhQIItgZwkUYpk7OuSpYKypBCEq9YvoR9+/Fq/lxHpdA1NHYqiKLjsx++37Ecj0u06bUTkqPhvmzH9XWQk2Wl1e9lULER9X5YXAozKcZJkt9Lc6aGxvQuL0vfHMDn6MEVXBMyeLhMTExOT4x2j6IoUF689nqQ/PjJtZFRiU4ZpVLdV9+h0aaKrURddkZIRZV+XUXSFc7qMfweXGHp8Hi0BcWhq9Ml+Jn3HbacP56LJedym9mgdDVgsoSmKQ/q4vNBmtTDFUF45MD3xhE0uPJEwRVcEzDldJiYmJibHOzGVFxpE2UXDL4rKmZCx8VXtVd32dIFeXvh1+ddUtlXisDqYlj0t7LYyKEOKrpr2Gmraa1BQGJ4aOEtKOl/G0AwQwRsen4cEW0KP125yeBiWlcwjl09iQFrkMtUjgSwxBMhLTYh53lc0TBukj00YfoKHaJwomKLLxMTExMTkBCU9Pp0Em+iriVZ02S12zh1yblT7D3C6eigvlKKr3dMOwLScacTb4sNuK50u6VS9v+99QMTJB/eZSacrOMFwX8M+7bgWxVwOmegYRVdfu1wSOSQZYPgJ3s91omD+V8bExMTExOQERVEUvj/6+0zLnsb4fuO73XZW/1lMy57GbZNv0+Lye8I4q6un8sKsxCyS4vQF7uzc8KWFoM/qOth0kBe3v8jD6x8G4LtDvxuy7YRMMSR3Z93OgDANKbrM0kKTYPqnJGiJhYer12rSwFQtFfJETy48UTBFl4mJiYmJyQnM7VNu59mzn8VhdXS7XbI9mWfPfpZrx10b9b5leWFlW2WPTpeiKAx2Ddb+jtTPBXps/O763fxl7V8AuGHcDVw/7vqQbXOTc8lLzsPr97KhaoN2v9HpMjEJ5tJpIjUz2vlhsZJot/GdMdkk2a3MHPztjp0wOTKYc7pMTExMTExMDgvS6drXsE8bOBzJ6QIYkjqEbbXbyEvO00oIw5HnzMOqWPH6vQD8ZOJP+PHEH0fsM5uWPY3SllLWVqzVxNy+RiG6hqV+uyEOnxR+wpu738SHDwDr/2/v3oOiOs8/gH93geV+CXJZVgTUWI1RiQhSptGQQATGUaO2IZSOlyRq0qVqsBmGZDSpveBoR/Mzw2injWKTjLfWCE1N4l1LIF7QjVEbIgyKF8CoheUit9339wfD0c3CLhgOh4XvZ2Zn4D3vOfucl8fjefac867KCelPpGN66PR+jYNsWzZ9FNKmhsHX3UW29/i/lyaj3WyW5ZkxGnj4V+5Gbm4ucnNzYTKZlA6FiIjIIQV7sUmVLQAAFptJREFUBAMAqhqrAHR8ybLGSdNt/8lBk1FQXoAZETNsTtThonbBOP9xuHT3ElZErcCrE1+1GUeMNgb55fk4W93xRdDt5nZU1FUA6Cj0+tPWr7dKU9V3ut9+n0XXAKNSqWQtuABA46yGhjedDRksurqh1+uh1+thNBrh69uze9eJiIjogc4rXZ26u7Ww09zH5yLCJwKRgZF2t/3+c++jpqkGEwIm2O0bo+34+pdLdy+hsa0R3zd9jzZzG9yc3DDca7jd9ftS5xW/pZOWoqW9BTsu75DaiGjwYnlNREREsvBz9YOz+sHnu7ZuLQQAJ7UTorXRcHGyf4Uh0COwRwUXYPlc1/nb56VbC0f6jlRs5sK4kDhEa7ueEp+IBh9e6SIiIiJZqFVqBLoHSrcXdvcdXf0hRhuDm2Udz3V1zpLYm5kLTeaOiTgengHxYc5qZ0Rro+1OSEJEQxOLLiIiIpJNoMeDosve7YVyitHGYH/ZfpytPotQ744vhe5N0bWrdBfWnV5ns8/s0bPxx6f/+KPiJKLBiUUXERERyaZz2njA/u2FcooO7riV79LdS/hfy/8AAKN9e150VTdWA+i4WvfDL5IWQuDS3UsoKC/AS2NfsvudZ0Q09Az6oqu0tBSpqakWv+/cuRMvvPCCglERERENDQ9PpqHkla7O57puNtzE9frrAB5tuvhZo2YhMzrTqv3twrdRUF6A9WfW4+8pf7c5+yIRDT2DfiKNsWPHwmAwwGAwoLCwEJ6ennj++eeVDouIiGhICPJ4cKVLyWe6AGCqdqr0s6uTK3Reuj7b9oqoFXB3dofhewO+uPpFn22XiAaHQV90PaygoAAJCQnw9PRUOhQiIqIhIdD9oStdCt5eCDyYOh7omLnQSe3UZ9sO8gjC4gmLAQCbSjahxdTSZ9smIseneNF18uRJzJo1CzqdDiqVCvv377fqk5ubi4iICLi5uSE2NhanT59+pPfas2ePxa2GREREJK+Hr3QpeXsh8OC5LqB3k2j01KInFyHIIwi3Gm/hw8sf/ujtmcwmNLU1dfsSQnS5nhDCol+rqbXH72kW5h8dNxFZU/yZrsbGRkRGRuLll1/GvHnzrJbv3r0bmZmZ2Lp1K2JjY/Hee+8hKSkJpaWlCArqOJA/9dRTaG+3/mLBgwcPQqfruHXAaDSiqKgIu3btshlPS0sLWloefDplNBp/zO4RERENaQ8XXf7u/gpGAoR4hSDUKxQ3Gm70ahKNnnJ3dsfKqJV4q/At/PXCX5E2Lk2anr63jK1GzM2fi9tNt7vtkxiWiE3PbrJoMwszfnXgV/jmzjdSm7PaGeunr8fz4bYfr3i78G2cqT6D/XP2w8PF45HiJqKuKX6lKyUlBX/4wx8wd+7cLpdv3LgRS5YsweLFizF+/Hhs3boVHh4e2LZtm9THYDDg4sWLVq/OggsA8vPzMWPGDLi5udmMJycnB76+vtJrxIgRfbOjREREQ1CYdxjGPDYGTw9/ekB8h1XauDQMcxuGhPAEWbY/c9RMeLl4oam9SZrx8FFU1FXYLLgAoLiq2Kqtsa3RouACgHZzO0pqSuy+Z0F5Aaoaq3Dw2sHeBUtEdil+pcuW1tZWlJSUIDs7W2pTq9VITExEcbH1gcaWPXv2YOnSpXb7ZWdnIzPzwaxERqORhRcREdEjcnFywT9n/VPpMCQLnlyABU8ukG37apUazuq+O70a7jUc++dYPnpxo/4G5hZ0/WH1w75M+xJ/++Zv2H5xe5/FQ0SPRvErXbbcuXMHJpMJwcHBFu3BwcGoru75p0d1dXU4ffo0kpKS7PZ1dXWFj48PPvzwQ/z0pz9FQoI8n4QRERENFSqVilOoPyIVVHBzdrN49fSKobuTO5xVA/rzdaIhY0AXXX3F19cXNTU10Gg0PV5Hr9fj8uXLOHPmjIyRERERERHRYDegi66AgAA4OTmhpqbGor2mpgZarVbW987NzcX48eMRExNjvzMREREREVE3BnTRpdFoMGXKFBw5ckRqM5vNOHLkCOLi4mR9b17pIiIiIiKivqD4jb4NDQ0oKyuTfq+oqIDBYIC/vz/CwsKQmZmJhQsXIjo6GlOnTsV7772HxsZGLF68WNa4cnNzkZubC5PJJOv7EBERERHR4KZ40XX27Fk8++yz0u+dMwcuXLgQeXl5SE1Nxffff481a9aguroaTz31FD7//HOryTX6ml6vh16vh9FohK+vr6zvRUREREREg5fiRVd8fHy336jeKSMjAxkZGf0UUQde6SIiIiIior4woJ/pUhKf6SIiIiIior7AoouIiIiIiEhGLLq6wSnjiYiIiIioL7Do6gZvLyQiIiIior6g+EQaA13nJB9Go1HhSIiIaLBrqG+A6b4Jbao2q/936o31MN03ob2tnf8nyaSlsQWm+yY01TdZjXFzQzNM901obmi2O/7tTe0wtZpQb6yHUW3Zt62pDab7JjTUN6CxrbHj791k/ffuzIV2tfXf21Yu1Ld2LAM6zl16E3fnel3tP1FvNdQbYW5pQtt9Uxc53ARzSxNMZrXD5VpnvPYmAvwhlejtGkPMjRs3MGLECKXDICIiIiKiAeL69esIDQ3tcX8WXXaYzWbcunUL3t7eUKlUisZiNBoxYsQIXL9+HT4+PorGMlhxjOXF8ZUfx1heHF/5cYzlxfGVH8dYXkqPrxAC9fX10Ol0UKt7/qQWby+0Q61W96qK7Q8+Pj78RywzjrG8OL7y4xjLi+MrP46xvDi+8uMYy0vJ8fX19e31OpxIg4iIiIiISEYsuoiIiIiIiGTk9O67776rdBDUc05OToiPj4ezM+8MlQvHWF4cX/lxjOXF8ZUfx1heHF/5cYzl5Yjjy4k0iIiIiIiIZMTbC4mIiIiIiGTEoouIiIiIiEhGLLqIiIiIiIhkxKKLiIiIiIhIRiy6HEhubi4iIiLg5uaG2NhYnD59WumQHFJOTg5iYmLg7e2NoKAgvPDCCygtLbXoEx8fD5VKZfF67bXXFIrYsbz77rtWYzdu3DhpeXNzM/R6PYYNGwYvLy/Mnz8fNTU1CkbseCIiIqzGWKVSQa/XA2D+9tbJkycxa9Ys6HQ6qFQq7N+/32K5EAJr1qxBSEgI3N3dkZiYiCtXrlj0uXfvHtLT0+Hj4wM/Pz+88soraGho6M/dGNBsjXFbWxuysrIwceJEeHp6QqfTYcGCBbh165bFNrrK+3Xr1vX3rgxI9nJ40aJFVmOXnJxs0Yc5bJu9Me7qmKxSqbBhwwapD3O4ez05N+vJ+UNlZSVmzpwJDw8PBAUF4c0330R7e3t/7kq3WHQ5iN27dyMzMxPvvPMOzp07h8jISCQlJeH27dtKh+ZwTpw4Ab1ej6+++gqHDh1CW1sbZsyYgcbGRot+S5YsQVVVlfRav369QhE7nieffNJi7AoLC6Vlb7zxBv71r39h7969OHHiBG7duoV58+YpGK3jOXPmjMX4Hjp0CADwi1/8QurD/O25xsZGREZGIjc3t8vl69evx+bNm7F161acOnUKnp6eSEpKQnNzs9QnPT0dly5dwqFDh/Dpp5/i5MmTWLp0aX/twoBna4ybmppw7tw5rF69GufOncO+fftQWlqK2bNnW/Vdu3atRV7/5je/6Y/wBzx7OQwAycnJFmO3c+dOi+XMYdvsjfHDY1tVVYVt27ZBpVJh/vz5Fv2Yw13rybmZvfMHk8mEmTNnorW1FUVFRdixYwfy8vKwZs0aJXbJmiCHMHXqVKHX66XfTSaT0Ol0IicnR8GoBofbt28LAOLEiRNS2zPPPCNWrFihYFSO65133hGRkZFdLqutrRUuLi5i7969Utt///tfAUAUFxf3V4iDzooVK8To0aOF2WwWQjB/fwwA4pNPPpF+N5vNQqvVig0bNkhttbW1wtXVVezcuVMIIcTly5cFAHHmzBmpz2effSZUKpW4efNm/wXvIH44xl05ffq0ACCuXbsmtYWHh4tNmzbJHZ7D62p8Fy5cKObMmdPtOszh3ulJDs+ZM0c899xzFm3M4Z774blZT84fDhw4INRqtaiurpb6bNmyRfj4+IiWlpb+3YEu8EqXA2htbUVJSQkSExOlNrVajcTERBQXFysY2eBQV1cHAPD397do//jjjxEQEIAJEyYgOzsbTU1NSoTnkK5cuQKdTodRo0YhPT0dlZWVAICSkhK0tbVZ5PK4ceMQFhbGXH5Era2t+Oijj/Dyyy9DpVJJ7czfvlFRUYHq6mqLnPX19UVsbKyUs8XFxfDz80N0dLTUJzExEWq1GqdOner3mAeDuro6qFQq+Pn5WbSvW7cOw4YNw+TJk7Fhw4YBc9uQIzh+/DiCgoIwduxYvP7667h79660jDnct2pqavDvf/8br7zyitUy5nDP/PDcrCfnD8XFxZg4cSKCg4OlPklJSTAajbh06VI/Rt81x/ka5yHszp07MJlMFkkEAMHBwfj2228VimpwMJvNWLlyJX72s59hwoQJUvsvf/lLhIeHQ6fT4cKFC8jKykJpaSn27dunYLSOITY2Fnl5eRg7diyqqqrwu9/9DtOmTcPFixdRXV0NjUZjdSIVHByM6upqhSJ2bPv370dtbS0WLVoktTF/+05nXnZ1/O1cVl1djaCgIIvlzs7O8Pf3Z14/gubmZmRlZSEtLQ0+Pj5S+/LlyxEVFQV/f38UFRUhOzsbVVVV2Lhxo4LROobk5GTMmzcPI0eORHl5Od566y2kpKSguLgYTk5OzOE+tmPHDnh7e1vdOs8c7pmuzs16cv5QXV3d5bG6c5nSWHTRkKbX63Hx4kWLZ44AWNzHPnHiRISEhCAhIQHl5eUYPXp0f4fpUFJSUqSfJ02ahNjYWISHh2PPnj1wd3dXMLLB6YMPPkBKSgp0Op3UxvwlR9XW1oYXX3wRQghs2bLFYllmZqb086RJk6DRaLBs2TLk5OTA1dW1v0N1KC+99JL088SJEzFp0iSMHj0ax48fR0JCgoKRDU7btm1Deno63NzcLNqZwz3T3bmZo+PthQ4gICAATk5OVjO01NTUQKvVKhSV48vIyMCnn36KY8eOITQ01Gbf2NhYAEBZWVl/hDao+Pn54Sc/+QnKysqg1WrR2tqK2tpaiz7M5Udz7do1HD58GK+++qrNfszfR9eZl7aOv1qt1mpSo/b2dty7d4953QudBde1a9dw6NAhi6tcXYmNjUV7ezuuXr3aPwEOIqNGjUJAQIB0TGAO953//Oc/KC0ttXtcBpjDXenu3Kwn5w9arbbLY3XnMqWx6HIAGo0GU6ZMwZEjR6Q2s9mMI0eOIC4uTsHIHJMQAhkZGfjkk09w9OhRjBw50u46BoMBABASEiJ3eINOQ0MDysvLERISgilTpsDFxcUil0tLS1FZWclcfgTbt29HUFAQZs6cabMf8/fRjRw5Elqt1iJnjUYjTp06JeVsXFwcamtrUVJSIvU5evQozGazVPCSbZ0F15UrV3D48GEMGzbM7joGgwFqtdrqtjiy78aNG7h79650TGAO950PPvgAU6ZMQWRkpN2+zOEH7J2b9eT8IS4uDt98843FBwidH+CMHz++f3bEFoUn8qAe2rVrl3B1dRV5eXni8uXLYunSpcLPz89ihhbqmddff134+vqK48ePi6qqKunV1NQkhBCirKxMrF27Vpw9e1ZUVFSI/Px8MWrUKDF9+nSFI3cMq1atEsePHxcVFRXiyy+/FImJiSIgIEDcvn1bCCHEa6+9JsLCwsTRo0fF2bNnRVxcnIiLi1M4asdjMplEWFiYyMrKsmhn/vZefX29OH/+vDh//rwAIDZu3CjOnz8vzZy3bt064efnJ/Lz88WFCxfEnDlzxMiRI8X9+/elbSQnJ4vJkyeLU6dOicLCQjFmzBiRlpam1C4NOLbGuLW1VcyePVuEhoYKg8FgcVzunHGsqKhIbNq0SRgMBlFeXi4++ugjERgYKBYsWKDwng0Mtsa3vr5e/Pa3vxXFxcWioqJCHD58WERFRYkxY8aI5uZmaRvMYdvsHSeEEKKurk54eHiILVu2WK3PHLbN3rmZEPbPH9rb28WECRPEjBkzhMFgEJ9//rkIDAwU2dnZSuySFRZdDuT9998XYWFhQqPRiKlTp4qvvvpK6ZAcEoAuX9u3bxdCCFFZWSmmT58u/P39haurq3j88cfFm2++Kerq6pQN3EGkpqaKkJAQodFoxPDhw0VqaqooKyuTlt+/f1/8+te/Fo899pjw8PAQc+fOFVVVVQpG7Ji++OILAUCUlpZatDN/e+/YsWNdHhMWLlwohOiYNn716tUiODhYuLq6ioSEBKtxv3v3rkhLSxNeXl7Cx8dHLF68WNTX1yuwNwOTrTGuqKjo9rh87NgxIYQQJSUlIjY2Vvj6+go3NzfxxBNPiD/96U8WRcNQZmt8m5qaxIwZM0RgYKBwcXER4eHhYsmSJVYf2jKHbbN3nBBCiL/85S/C3d1d1NbWWq3PHLbN3rmZED07f7h69apISUkR7u7uIiAgQKxatUq0tbX18950TSWEEDJdRCMiIiIiIhry+EwXERERERGRjFh0ERERERERyYhFFxERERERkYxYdBEREREREcmIRRcREREREZGMWHQRERERERHJiEUXERERERGRjFh0ERERERERyYhFFxERDSnx8fFYuXKl0mEQEdEQohJCCKWDICIi6i/37t2Di4sLvL29ERERgZUrV7IIIyIiWTkrHQAREVF/8vf37/Nttra2QqPR9Pl2iYhocODthURENKR03l4YHx+Pa9eu4Y033oBKpYJKpZL6FBYWYtq0aXB3d8eIESOwfPlyNDY2SssjIiLw+9//HgsWLICPjw+WLl2K1tZWZGRkICQkBG5ubggPD0dOTo4Su0hERAMMiy4iIhqS9u3bh9DQUKxduxZVVVWoqqoCAJSXlyM5ORnz58/HhQsXsHv3bhQWFiIjI8Ni/T//+c+IjIzE+fPnsXr1amzevBkFBQXYs2cPSktL8fHHHyMiIkKBPSMiooGGtxcSEdGQ5O/vDycnJ3h7e0Or1UrtOTk5SE9Pl57zGjNmDDZv3oxnnnkGW7ZsgZubGwDgueeew6pVq6T1KisrMWbMGDz99NNQqVQIDw/v3x0iIqIBi1e6iIiIHvL1118jLy8PXl5e0ispKQlmsxkVFRVSv+joaIv1Fi1aBIPBgLFjx2L58uU4ePBgf4dOREQDFK90ERERPaShoQHLli3D8uXLrZaFhYVJP3t6elosi4qKQkVFBT777DMcPnwYL774IhITE/GPf/xD9piJiGhgY9FFRERDlkajgclksmiLiorC5cuX8fjjj/d6ez4+PkhNTUVqaip+/vOfIzk5Gffu3ZNlxkQiInIcvL2QiIiGrIiICJw8eRI3b97EnTt3AABZWVkoKipCRkYGDAYDrly5gvz8fKuJNH5o48aN2LlzJ7799lt899132Lt3L7RaLfz8/PpjV4iIaABj0UVEREPW2rVrcfXqVYwePRqBgYEAgEmTJuHEiRP47rvvMG3aNEyePBlr1qyBTqezuS1vb2+sX78e0dHRiImJwdWrV3HgwAGo1fyvlohoqFMJIYTSQRAREREREQ1W/PiNiIiIiIhIRiy6iIiIiIiIZMSii4iIiIiISEYsuoiIiIiIiGTEoouIiIiIiEhGLLqIiIiIiIhkxKKLiIiIiIhIRiy6iIiIiIiIZMSii4iIiIiISEYsuoiIiIiIiGTEoouIiIiIiEhG/w/QZbgDNUysZwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(10,4), dpi=100).set_facecolor('white')\n",
    "for name, grad_norms in gradient_norms.items():\n",
    "    pyplot.plot(grad_norms, label=name)\n",
    "pyplot.xlabel('iters')\n",
    "pyplot.ylabel('gradient norm')\n",
    "pyplot.yscale('log')\n",
    "pyplot.legend(loc='best')\n",
    "pyplot.title('Gradient norms during SVI');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the learned parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weights = [0.375 0.625]\n",
      "locs = [ 0.49887404 10.984463  ]\n",
      "scale = 0.651433706284\n"
     ]
    }
   ],
   "source": [
    "map_estimates = global_guide(data)\n",
    "weights = map_estimates['weights']\n",
    "locs = map_estimates['locs']\n",
    "scale = map_estimates['scale']\n",
    "print('weights = {}'.format(weights.data.numpy()))\n",
    "print('locs = {}'.format(locs.data.numpy()))\n",
    "print('scale = {}'.format(scale.data.numpy()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model's `weights` are as expected, with about 2/5 of the data in the first component and 3/5 in the second component. Next let's visualize the mixture model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.arange(-3,15,0.1)\n",
    "Y1 = weights[0].item() * scipy.stats.norm.pdf((X - locs[0].item()) / scale.item())\n",
    "Y2 = weights[1].item() * scipy.stats.norm.pdf((X - locs[1].item()) / scale.item())\n",
    "\n",
    "pyplot.figure(figsize=(10, 4), dpi=100).set_facecolor('white')\n",
    "pyplot.plot(X, Y1, 'r-')\n",
    "pyplot.plot(X, Y2, 'b-')\n",
    "pyplot.plot(X, Y1 + Y2, 'k--')\n",
    "pyplot.plot(data.data.numpy(), np.zeros(len(data)), 'k*')\n",
    "pyplot.title('Density of two-component mixture model')\n",
    "pyplot.ylabel('probability density');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally note that optimization with mixture models is non-convex and can often get stuck in local optima. For example in this tutorial, we observed that the mixture model gets stuck in an everthing-in-one-cluster hypothesis if `scale` is initialized to be too large.\n",
    "\n",
    "## Serving the model: predicting membership\n",
    "\n",
    "Now that we've trained a mixture model, we might want to use the model as a classifier. \n",
    "During training we marginalized out the assignment variables in the model. While this provides fast convergence, it prevents us from reading the cluster assignments from the guide. We'll discuss two options for treating the model as a classifier: first using [infer_discrete](http://docs.pyro.ai/en/dev/inference_algos.html#pyro.infer.discrete.infer_discrete) (much faster) and second by training a secondary guide using enumeration inside SVI (slower but more general).\n",
    "\n",
    "### Predicting membership using discrete inference\n",
    "\n",
    "The fastest way to predict membership is to use the [infer_discrete](http://docs.pyro.ai/en/dev/inference_algos.html#pyro.infer.discrete.infer_discrete) handler, together with `trace` and `replay`. Let's start out with a MAP classifier, setting `infer_discrete`'s temperature parameter to zero. For a deeper look at effect handlers like `trace`, `replay`, and `infer_discrete`, see the [effect handler tutorial](http://pyro.ai/examples/effect_handlers.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0, 0, 1, 1, 1])\n"
     ]
    }
   ],
   "source": [
    "guide_trace = poutine.trace(global_guide).get_trace(data)  # record the globals\n",
    "trained_model = poutine.replay(model, trace=guide_trace)  # replay the globals\n",
    "    \n",
    "def classifier(data, temperature=0):\n",
    "    inferred_model = infer_discrete(trained_model, temperature=temperature,\n",
    "                                    first_available_dim=-2)  # avoid conflict with data plate\n",
    "    trace = poutine.trace(inferred_model).get_trace(data)\n",
    "    return trace.nodes[\"assignment\"][\"value\"]\n",
    "\n",
    "print(classifier(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed we can run this classifer on new data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_data = torch.arange(-3, 15, 0.1)\n",
    "assignment = classifier(new_data)\n",
    "pyplot.figure(figsize=(8, 2), dpi=100).set_facecolor('white')\n",
    "pyplot.plot(new_data.numpy(), assignment.numpy())\n",
    "pyplot.title('MAP assignment')\n",
    "pyplot.xlabel('data value')\n",
    "pyplot.ylabel('class assignment');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To generate random posterior assignments rather than MAP assignments, we could set `temperature=1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "tensor([0, 0, 1, 1, 1])\n"
     ]
    }
   ],
   "source": [
    "print(classifier(data, temperature=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the classes are very well separated, we zoom in to the boundary between classes, around 5.75."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_data = torch.arange(5.5, 6.0, 0.005)\n",
    "assignment = classifier(new_data, temperature=1)\n",
    "pyplot.figure(figsize=(8, 2), dpi=100).set_facecolor('white')\n",
    "pyplot.plot(new_data.numpy(), assignment.numpy(), 'bx', color='C0')\n",
    "pyplot.title('Random posterior assignment')\n",
    "pyplot.xlabel('data value')\n",
    "pyplot.ylabel('class assignment');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predicting membership by enumerating in the guide\n",
    "\n",
    "A second way to predict class membership is to enumerate in the guide. This doesn't work well for serving classifier models, since we need to run stochastic optimization for each new input data batch, but it is more general in that it can be embedded in larger variational models.\n",
    "\n",
    "To read cluster assignments from the guide, we'll define a new `full_guide` that fits both global parameters (as above) and local parameters (which were previously marginalized out). Since we've already learned good values for the global variables, we will block SVI from updating those by using [poutine.block](http://docs.pyro.ai/en/dev/poutine.html#pyro.poutine.block)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "@config_enumerate\n",
    "def full_guide(data):\n",
    "    # Global variables.\n",
    "    with poutine.block(hide_types=[\"param\"]):  # Keep our learned values of global parameters.\n",
    "        global_guide(data)\n",
    "\n",
    "    # Local variables.\n",
    "    with pyro.plate('data', len(data)):\n",
    "        assignment_probs = pyro.param('assignment_probs', torch.ones(len(data), K) / K,\n",
    "                                      constraint=constraints.unit_interval)\n",
    "        pyro.sample('assignment', dist.Categorical(assignment_probs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "...................................................................................................\n",
      "..................................................................................................."
     ]
    }
   ],
   "source": [
    "optim = pyro.optim.Adam({'lr': 0.2, 'betas': [0.8, 0.99]})\n",
    "elbo = TraceEnum_ELBO(max_plate_nesting=1)\n",
    "svi = SVI(model, full_guide, optim, loss=elbo)\n",
    "\n",
    "# Register hooks to monitor gradient norms.\n",
    "gradient_norms = defaultdict(list)\n",
    "svi.loss(model, full_guide, data)  # Initializes param store.\n",
    "for name, value in pyro.get_param_store().named_parameters():\n",
    "    value.register_hook(lambda g, name=name: gradient_norms[name].append(g.norm().item()))\n",
    "\n",
    "losses = []\n",
    "for i in range(200 if not smoke_test else 2):\n",
    "    loss = svi.step(data)\n",
    "    losses.append(loss)\n",
    "    print('.' if i % 100 else '\\n', end='')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(10,3), dpi=100).set_facecolor('white')\n",
    "pyplot.plot(losses)\n",
    "pyplot.xlabel('iters')\n",
    "pyplot.ylabel('loss')\n",
    "pyplot.yscale('log')\n",
    "pyplot.title('Convergence of SVI');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pyplot.figure(figsize=(10,4), dpi=100).set_facecolor('white')\n",
    "for name, grad_norms in gradient_norms.items():\n",
    "    pyplot.plot(grad_norms, label=name)\n",
    "pyplot.xlabel('iters')\n",
    "pyplot.ylabel('gradient norm')\n",
    "pyplot.yscale('log')\n",
    "pyplot.legend(loc='best')\n",
    "pyplot.title('Gradient norms during SVI');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now examine the guide's local `assignment_probs` variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "assignment_probs = pyro.param('assignment_probs')\n",
    "pyplot.figure(figsize=(8, 3), dpi=100).set_facecolor('white')\n",
    "pyplot.plot(data.data.numpy(), assignment_probs.data.numpy()[:, 0], 'ro',\n",
    "            label='component with mean {:0.2g}'.format(locs[0]))\n",
    "pyplot.plot(data.data.numpy(), assignment_probs.data.numpy()[:, 1], 'bo',\n",
    "            label='component with mean {:0.2g}'.format(locs[1]))\n",
    "pyplot.title('Mixture assignment probabilities')\n",
    "pyplot.xlabel('data value')\n",
    "pyplot.ylabel('assignment probability')\n",
    "pyplot.legend(loc='center');"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
